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This paper estimates a job search model with savings on Danish micro data that include observations on wealth and wages. Controlling for extensive observed and unobserved worker characteristics heterogeneity, the estimation relates observed unemployment spells to the model implied hazard rate for each worker. The model estimates are sensible and fit the data well. Optimal UI policy is determined in the estimated model as a trade-off between insurance provision and distortion of search incentives. The analysis emphasizes an important policy sensitivity to the interest rate and the importance of including transitional dynamics in the analysis.

The paper estimates a job search model with savings on Danish unemployment spell data and determines optimal unemployment benefit levels for the estimated model. In the model, an unemployed worker decides on how intensely to search for a new job based on a comparison of the marginal search cost and the net gain of moving from unemployment into employment. The worker can insure against income fluctuations through savings but the insurance will necessarily be imperfect due to the nature of the income process, imperfect asset markets, and the presence of borrowing constraints. Unemployment benefits provide additional insurance but adversely affect the worker’s incentives to search for employment. The optimal policy study is focused on the trade-off between providing insurance beyond the worker’s ability to self-insure through savings and the adverse impact on the worker’s job search incentives. The core of the identification of the model is based exactly on these relationships by relating the worker’s observed savings,ship between the choice of search intensity and savings.1 Furthermore, for a given benefit level data show a U-shaped relationship between unemployment duration and the wage level of the worker.While not widely recognized, this type of relationship is quite natural in a sequential job search model with savings where shifts of the wage offer distribution imply both substitution and income effects with opposing impacts on the search decision.2 Both of these relationships are robust to conditioning on observed and unobserved worker characteristics. They are both important identifiers of the curvature of the utility of consumption function. The estimate implies a constant relative risk aversion coefficient of 2.21.The role of unemployment benefits is in the paper purely one of providing insurance against consumption fluctuations at the cost of distorting search incentives.3 Papers such as Baily (1978), Flemming (1978), Hansen and Imrohoroglu (1992), andWang andWilliamson (2002) have studied this question in models with savings. However, it is a common feature of these papers as well as the broader literature on optimal unemployment insurance that the use of savings as a self insurance instrument has been seriously curtailed. In studies where savings are allowed, the return to savings is often set at such a low rate that holding savings is costly and consequently the option to use savings as a self-insurance instrument has low value.I find that the optimal benefit policy is highly sensitive to the relationship between the interest rate and the subjective discount rate. Specifically, the optimal benefit level ranges from a 43% replacement rate for an interest rate almost equal to the subjective discount rate to an 82% replacement rate for a zero interest rate. The sensitivity of savings to the level of the interest rate is a well known result in the consumption-savings literature. However since savings and unemployment insurance are not often studied together, the high sensitivity of unemployment insurance design to the interest rate and subjective discount rate is rarely emphasized.As also argued in Joseph and Weitzenblum (2003), rather than simply comparing steady states, I find that once savings are included in the optimal policy analysis, one must include transitional dynamics in order to avoid a serious downward bias in the optimal unemployment benefit results. I quantify the downward bias which can be as large as 10 percentage points in the optimal replacement rate.The analysis of the job search model with savings is complicated by the inability to establish global concavity of the value functions. Danforth (1979) shows that in the special case where employment is an absorbing state, one can characterize the reservation wage choice in relation to the degree of absolute risk aversion of the utility function. In the case of decreasing absolute risk aversion, the reservation wage choice will be increasing in wealth. Flemming(1978) and Acemoglu and Shimer (1999) are examples of the constant absolute risk aversion case combined with the assumption that search costs are monetary, and that there is no lower bound on wealth.4 In this case, the search choice is unaffected by wealth and the results for this special case do generalize to the case in which employment is not an absorbing state. However in general, once employment is no longer an absorbing state, construction of characterization theorems of the worker’s search and savings choices is made difficult because the value functions may not be globally concave. Lentz and Tranæs (2005) establish characterization theorems for the search intensity model for the more general case where search costs can be non-monetary. The paper is structured as follows. In Section 2 the model and its key characteristics are presented. Section 3 presents the estimation strategy, data, and estimation results. Based on the results of the estimation, the paper proceeds by determining optimal benefit levels at an individual level in Section 4.1 and Section 4.2 considers optimal group wide insurance schemes. Finally, Section 5 concludes. unemployment benefits, and earnings when employed to observed unemployment durations. The model estimation successfully captures the key relationships in the data. Notably, wealthier individuals are observed to experience longer unemployment durations which is explained by the model throughm a negative relation-

This paper has estimated a job search model with savings and subsequently determined optimal benefit policy for the estimated model. Depending on the cost of self-insuring via savings, the optimal replacement rate ranges between 43% and 82%. If savings carry a low return relative to the subjective discount rate, self-insurance via savings will be expensive and consequently workers will want to rely more on unemployment benefit insurance to guard against income fluctuations. As a comparison, the actual replacement rate of the median income worker is around 50%. Thus,the level of the actual policy is within the range of optimal policy. However, the analysis does show, that the optimal replacement rate is almost constant across income levels which is in stark contrast with the current Danish system where replacement rates vary significantly across income levels. The observed 90% replacement rates for low income workers and the very low replacement rates for high income workers are not supported by the optimal policy study.The analysis also studied sensitivity to counter factual levels of moral hazard. It was shown that at higher levels of moral hazard, the optimal replacement rate drops to as low as 14% as workers switch into savings as their main insurance vehicle.The estimation strategy relates observed unemployment durations to the model implied unemployment hazard rate which the worker can affect by the choice of search intensity. Data show a positive relationship between wealth holdings and unemployment duration which the model successfully captures as a result of worker search behavior; wealthier workers search less. The U-shaped relationship between unemployment duration and the worker’s wage is also successfully captured as a straightforward search choice response to variation in wage expectations in a search model with savings. The savings aspect is important in this respect since search models without savings cannot generate a non-monotone relationship between the search choice and the wage. The relationships between unemployment duration and other worker characteristics are explained as a combination of a market effect captured in the individual offer arrival function parameter λ and the worker’s search response to the market effect.The estimated utility of consumption function implies a constant relative risk aversion coefficient of 2.21 and the estimated search cost function implies moderate hazard rate responses to changes in incentives.While Danish workers respond to changes in economic incentives in ways that are consistent with the model, the observed unemployment hazard rate response is modest in magnitude for the observed changes in incentives. As a consequence, while the model does imply positive duration dependence of the unemployment hazard rate, it will likely be dominated by other effects. Indeed, most duration dependence analyses show a slightly negative or zero trend in the baseline hazard rate over unemployment duration.The policy analysis emphasized the importance of including transitional dynamics in the analysis. Failure to do so, will introduce a significant downward bias in the results because the wealth distribution in the economy depends on the benefit scheme. A lower level of benefits will result in greater wealth holdings in steady state. By not including transitional dynamics in the analysis one will be ignoring the consumption cost associated with building these greater wealth holdings and consequently lower benefit levels look more attractive. The analysis showed that the downward bias can be quite large even in the case where the interest rate is zero and the steady state wealth distribution is less sensitive to the benefit scheme.