بیمه بیکاری و انباشت سرمایه

In this paper, I examine a model economy with production, search, and unemployment insurance. The introduction of capital into the economy of Wang and Williamson (J. Monetary Econom. 49(7)(2001)1337) generates the result that optimal replacement ratios are always zero. The result arises from the decline in aggregate activity caused by unemployment insurance: both capital and labor inputs to production fall when benefits rise. Unlike most of the literature, I compute explicitly the cost of the transition path; agents are made better off by switching to a steady state with no unemployment insurance, but the welfare gain is approximately cut in half. Only the very poor and unemployed suffer welfare losses along the transition path. I then briefly investigate the implications of negative replacement ratios.

The optimal provision of unemployment insurance (UI) in dynamic economies has generated a large body of literature, beginning with Shavell and Weiss (1979). However, much of the literature abstracts from the production side of the economy, instead choosing to ignore private savings entirely or to simply allow savings in the form of stored consumption.1 In general, it has been (at least implicitly) assumed that the introduction of endogenous interest and wage rates would add little insight into the role of unemployment insurance and would make little quantitative difference, and also therefore that capital accumulation is unimportant. The main purpose of this paper is to examine whether these assumptions are innocuous. The model economy here extends the model in Wang and Williamson (2001) to include firms, capital, and endogenous prices for labor and capital. Other papers have examined the role played by UI in models with capital markets; these papers include Costain (1997) and Heer (2002). However, those papers introduce other complicating features as well: wage contracting, thin and thick market externalities, and finite horizons with retirement. In those papers, it is not clear where exactly the benefit from unemployment insurance comes from: is it beneficial because it alleviates these labor market frictions or because it overcomes some capital market incompleteness? This paper retains one labor market friction—the costly and unobservable search which leads to moral hazard—but otherwise abstracts from the details of the labor market. The purpose of this abstraction is to isolate attention on the role unemployment insurance can play in mitigating the effects of a missing market. The literature finds a wide range of optimal replacement ratios (defined variously as that maximizing average welfare or the welfare of a newborn). For example, Hansen and İmrohorogˇlu (1992) finds that the optimal permanent replacement ratio ranges from 0.65 in the absence of moral hazard to 0.05 in a case with extreme moral hazard. Sleet (1997), in a model quite similar to this one but without capital, finds an optimal value of 0.4. Wang and Williamson (2001) computes the optimal replacement ratio for benefits that last only two quarters; they obtain a value of 0.47. Davidson and Woodbury (1997) finds an even stronger result: the optimal replacement ratio is 1 if benefits are given for a short duration and around 0.5 if unlimited. Costain (1997) and Heer (2002) instead choose to maximize the utility of a newborn agent—they find that optimal replacement ratios are typically around 0.5 for benefits that are limited in duration. In contrast, the results in this paper point to an optimal replacement ratio of zero independent of the duration. The welfare gain from eliminating the current system is 1.1 percent of aggregate consumption, a number which is somewhat larger than those found in the literature, and 0.59 percent of consumption if the transition is taken into account. The essence of the zero replacement ratio result comes down to UI's effect on the capital and labor inputs. The effect that unemployment insurance has on the labor input has been widely studied. In this model, UI benefits can increase the exit rate from employment (the separation effect) as well as decrease the exit rate from unemployment (the attachment effect). By lowering the cost of unemployment, benefits make it more likely that agents will not exert enough effort to find a job or retain one they already have. All the papers cited above include the second effect; many, however, assume that the separation effect is negligible or even zero. However, there is more to the story than just the labor input. Aggregate savings in our model will equal the demand for capital in equilibrium. As a result, unemployment insurance can have an impact on the aggregate level of capital. As the labor input falls, so will the marginal product of capital. In addition, increasing unemployment insurance directly reduces the demand for precautionary savings. Consequently, aggregate savings will fall, reducing the capital input. When combined with the decline in the labor input, the result is a relatively large decline in aggregate activity, whether measured by output, consumption, or investment. The potential consumption smoothing benefits of unemployment insurance will be swamped by these effects; it should be noted that UI fails to smooth consumption in this economy—the standard deviation of lifetime consumption rises from 0.0749 to 0.0805 in the presence of the calibrated income support system and the innovation to consumption at the onset of an unemployment spell changes from -0.063-0.063 to -0.081-0.081. In addition, the tight link between savings and output is critical; without such a link, unemployment insurance has positive welfare effects. This result is robust to the elimination of the separation effect mentioned above; it holds even when all separations are exogenous. This particular robustness result is important as there appears to be little evidence that the separation effect is very strong. Furthermore, when I examine the transition explicitly, the finding is that almost all agents are made better off; this transition would be implemented in a majority voting environment.2 However, not all agents gain the same amount from the transition; the relatively-poor but still well-insured have the highest gain, with the poor and the wealthy gaining relatively less. Only the very poor and unemployed lose utility. Of particular importance for aggregate welfare analysis is the skewness of the wealth distribution; the number of relatively poor agents, and their corresponding high marginal utilities of consumption, is critical in assessing the potential welfare effects of unemployment insurance. In models with storage, where the exogenous interest rate is always below the time rate of preference, agents tend to cluster at the upper end of the distribution—see Fig. 1 in Wang and Williamson (2001). This contrasts with the empirical wealth distribution in the US, where there are far more poor agents than rich agents (see Table 3 in Quadrini and Ríos-Rull (1997)). The model examined here produces a wealth distribution which is a better qualitative match for the empirical US distribution than much of the literature.It is appropriate here to discuss what the model cannot do. This model has a degenerate wage distribution; consequently, workers do not search to find better jobs. This dimension, which is one first proposed by Albrecht and Axell (1984) and later extended by Acemoglu and Shimer (2000), is completely absent. In those papers, UI can improve efficiency by raising the quality of matches. Whether this effect is quantitatively large enough to counteract the issues raised here is unknown, but is the subject of ongoing work. Very preliminary results suggest that UI has a more positive role to play in economies with permanent differences in productivity and segmented labor markets, however, pointing to the possibility that these results do not generalize in that direction. The paper is organized as follows. Section 2 presents the model. This section also presents the derivation of the first-best allocation (one in which there is no moral hazard problem). Section 3 calibrates the model to US data and presents results from the benchmark economy and Section 4 presents the welfare results. The transition path to the no-government steady state is computed in Section 5. Section 6 discusses the possibility that the true optimal replacement ratio might be negative. Section 7 concludes.

This paper examined the nature of optimal unemployment insurance in a model with production and private savings. Unlike most of the literature, production in this economy takes place at a firm using both capital and labor as inputs, resulting in endogenous interest and wage rates. The resulting optimum rate of benefits is zero for a wide range of economies, even when the cost of the transition is taken into account. I have conducted extensive sensitivity analysis for my results. In particular, the optimality of zero unemployment insurance is robust to different preference parameters, different tax bases, and transactions costs in the asset market, provided they are not very large. One experiment which is particularly useful to report involves the aggregate stock of capital, which I calibrated to be 11.5 times GDP. If instead I calibrate this to a smaller number that does not include the value of residential housing or consumer durables, I get a number of about 8.35 times GDP. When ββ and δδ are set consistent with this value, the value of eliminating UI rises to 1.7 percent of consumption due to a larger increase in capital. Of course, my results do not come without some reservations. In particular, I have abstracted from some features of the labor market that apparently have some importance. For example, Costain (1997) introduces “thick’’ and “thin’’ market externalities—the number of searchers on each side of the market influences the probability any one agent will find a job. Unemployment insurance can mitigate the consequences of these externalities by limiting the number of searchers, particularly from the supply side of the labor market. It would appear that the main benefit from UI is gained through this channel and not through its effect on capital market imperfections.25 Furthermore, market wages do not have the degenerate distribution assumed here; there is considerable dispersion in real wages in the US economy. With a nondegenerate wage distribution, UI tends to subsidize the low-income workers (who do not search as hard) at the expense of the high-income workers. However, a complicating feature is that benefits are tied to past wages which, as in Ljungqvist and Sargent (1998), would lead to households with high past wages but poor current prospects not searching enough. Furthermore, there is the possibility that UI affects the accumulation of human capital—since wages tend to decline with unemployment duration and UI tends to extend the duration of unemployment spells, there may be additional effects related to the productivity of the workforce. Finally, with dispersion in wages, workers may also view UI as a financing tool for them to find a better match, as in Acemoglu and Shimer (2000). It is not clear what the ultimate effect of introducing wage dispersion into this model would be, but it clearly seems important. Lastly, segmentation in labor market opportunities could be important; UI could aid the relatively-unskilled by keeping skilled workers out of unskilled jobs, a sort of underemployment insurance. There may also be important features related to the take-up rate of benefits. As mentioned by Gruber (1999), it is possible that there is a stigma attached to unemployment insurance for some groups of households which could explain why take-up rates in the US are around 67 percent (see Blank and Card, 1991). This stigma would likely apply only to high-wealth households.26 However, low-wealth households might have to deal with the pecuniary costs of UI take-up, such as the cost of travel—admittedly this constraint seems unlikely to be important now that states have enacted phone and web-enabled UI. Given that the moral hazard of agents with sufficiently high costs of take-up would disappear, it could be the case that positive UI would be optimal in this model. Finally, unemployment insurance may be an effective tool in combatting aggregate movements in income, rather than idiosyncratic ones. However, extensions to this model which allow for aggregate fluctuations are computationally infeasible, so this question must be postponed. Alternatively, since a large segment of the population saves using fiat money, unemployment insurance might help combat inflation costs; studying such a model would also be computationally demanding.