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In this study, we ask whether the presence of precautionary savings substantially reduces the optimal replacement rate in an European economy type characterized by high unemployment benefits and moral hazard. We build a simple job search model calibrated on French data and, in line with previous studies, find that the optimality criterion based on comparisons of steady states leads to a low optimal ratio. Yet, this result ignores potential transitional costs due to the necessity for agents to increase their savings and reduce their consumption whenever the ratio is cut. We therefore build a dynamic model taking full account of the transition, and show that a reduction in benefits reduces welfare. Even though the long-run optimal replacement rate is lower than the current one, transitional costs dominate long-run gains.

The purpose of this paper is to study the effect of a reduction in unemployment benefits when risk adverse individuals are subject to idiosyncratic employment shocks, cannot borrow, but can accumulate wealth to smooth their consumption. We argue that even in an economy characterized by a low steady state optimal replacement rate, such a policy could reduce welfare when the transition between steady states is taken into account. The analysis of unemployment insurance (UI) has given rise to a rich empirical literature on the potential moral hazard effect of unemployment benefits. However, no true consensus has been found, as to the quantitative impact of benefits on unemployment (Atkinson and Micklewright, 1991; Holmlund, 1998). Other studies have pointed out that unemployment insurance significantly helps agents smooth their consumption, at least for those who are often liquidity-constrained (see Gruber, 1997 or Browning and Crossley, 2001). The first theoretical models have addressed the trade-off between insurance and efficiency through analytical models in which saving was precluded (Shavell and Weiss, 1979 and Hopenhayn and Nicolini, 1997). They show that the optimal time-profile of benefits is decreasing over time. 3 In these approaches, agents are risk-averse, but have access neither to financial markets, nor to a storage technology. When allowing for access to financial markets, agents are inclined to accumulate assets as a precautionary device. Deaton (1991) shows that even low asset buffer stocks considerably help smooth consumption. Therefore, assessing the optimal level of benefits ought to take this self- insurance mechanism into account. Hansen and Imrohoroglu (1992) describe an economy where agents face exogenous idiosyncratic employment shocks, can neither borrow nor have access to a private insurance market, but can accumulate a non-interest-bearing asset. Moral hazard is modeled by the possibility for unemployed agents to accept or reject job offers and, in case of rejection, continue to receive benefits unless being detected, which occurs with a probability less than one. Costain (1997) builds a dynamic general equilibrium job search model with endogenous search intensity. His numerical simulations lead to a low value for the optimal insurance scheme. Indeed, a low replacement rate is not too costly in terms of insurance, since agents can self-insure through their precautionary savings. However, the welfare gains are quite small, because the actual and the optimal replacement rate are quite close (see also Wang and Williamson, 1999). In all these papers, the optimal level of unemployment benefits is determined by comparing different steady state equilibria corresponding to different UI schemes in the US context. We here intend to model explicitly the transition between steady states, in order to verify whether the previous results still hold. We consider a simple model of job search, as presented by Mortensen (1986), with full moral hazard. 4 Workers can save or dissave, but cannot borrow, and when unemployed, choose their search intensity. This specification departs from that of Hansen and Imrohoroglu, 1992, as we do not assess the impact of the degree of moral hazard on welfare, but simply take the absence of monitoring as given. The model is calibrated to fit the segment of low-paid jobs in the French labor market, featuring high unemployment and quite generous UI. In this context, the efficiency gains are potentially large. Therefore, the transition should be somewhat more pronounced than in a US model, where the long-run optimal replacement rate and the current one seem quite close to each other. Besides, we adopt an endogenous search effort rather than an accept–reject choice combined with a constant job offer arrival rate. This is motivated by the observation that the job rejection rates are very small in Western European countries (see van den Berg, 1990). Applying the usual steady state optimality criterion, welfare is maximized for a level of benefits markedly lower than its current level. As expected, the welfare gains associated with the long-run optimal replacement rate are then significant, and higher than in US models. However, this result does not take into account the potential costs or gains which arise until a new equilibrium is reached. Indeed, during the transition from high to low benefits, agents will be incited to reduce their consumption to increase their average savings up to their new long-run desired level. We then proceed our analysis by quantifying this adjustment cost. For this purpose, we construct the dynamic model which takes the non- stationarity of the equilibrium variables and the behavior rules into account, and simulate the impact of a cut in benefits, starting with initial given conditions. It appears that the adjustment costs dominate the long-run gains, so that a reduction in benefits, be it large or small, is always welfare-reducing. Results from long-run equilibrium comparisons may therefore be misleading, since they value the long-run gains from self-insurance, but not the accumulation path toward the steady state. This paper is organized as follows. Section 2 presents the model and the definition of the steady state equilibrium. Section 3 discusses the calibration. In Section 4, we determine the optimal level of unemployment benefits by comparing steady states. Section 5 computes the transition-adjusted welfare gains or losses due to a change in the replacement rate. Section 6 concludes.

In line with some previous studies, this article quantitatively assesses the optimal replacement rate in a model of unemployment, moral hazard and precautionary savings. As agents can partly self-insure against unemployment risk, the long-run optimal replacement rate is quite low. Calibrated on French data, the steady-state model, which baseline is characterized by high unemployment, high benefits, and high disincentive effects, suggests that the replacement rate should be significantly reduced. However, this result rests on steady-state comparisons, and ignore potential adjustment costs. Indeed, if a reduction in benefits yields welfare gains in the long-run, this is mostly due to the fact that agents are richer on average, since the precautionary motive is stronger. Reaching the steady-state distribution takes time and requires agents to reduce temporarily their consumption. Whether a reduction in the generosity of the public insurance scheme is really welfare-improving depends on how large transition costs and long-run gains are. When modeling explicitly the transition, it appears that a reduction in benefits is neither welfare-improving nor supported by a majority of agents, although the potential efficiency gains from a cut in benefits have been purposely set on the upper part of the estimated range. Sensitivity tests (Joseph and Weitzenblum, 2001) indicate that, when agents suffer less from consumption variability, the transitional costs are reduced. For a very low risk aversion, they can even disappear, but in this case agents are so inclined to undergo large changes in consumption that they hardly save on precautionary grounds. However, for substantially higher interest rates (1% quarterly and above), a reduction in the replacement rate does generate welfare gains. Indeed, steady state comparisons show that a reduction in benefits induces a considerable increase in asset income, and therefore in aggregate consumption. Long-run gains of a small reduction in benefits are then substantial, and, in such cases, dominate transitional costs.