EFFICIENT UNEMPLOYMENT INSURANCE: A Dynamic Model Without Wealth Effects 3

Optimal Consumption Decisions and Value Functions

We begin by defining Bellman values for employed, unemployed, and nonparticipating workers. We focus on steady state equilibria in which wages, capital stocks, queue lengths, and unemployment rates are constant. Let E(A,w) be the lifetime utility of a worker who is employed at wage w with assets A at the start of the time period. Similarly, let J(At w,q) be the expected value of an unemployed worker if he applies for wage w with queue length q in this period, and then follows an optimal consumption rule and application strategy thereafter. Let U(A) denote the Bellman value of an unemployed participant with assets A. Finally, define N(A,x) as the utility of a nonparticipating agent with asset level A} receiving home-produced income x.
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EFFICIENT UNEMPLOYMENT INSURANCE: A Dynamic Model Without Wealth Effects 2

Preferences and Technology

Consider an infinite horizon economy in discrete time. Each worker i makes consumption and job search decisions to maximize:

where сц is consumption at time t, f3 < 1 is the discount factor, and 9 > 0 is the coefficient of absolute risk aversion. Firms maximize the expected value of profits, discounted at the constant gross interest rate R > 1.

The search and production technologies are generalizations of the static model. At the start of a period firms may be either inactive, vacant, or have a filled job. Similarly, workers may either be unemployed or employed. Inactive firms can create a vacancy by buying perfectly durable capital at a unit cost conveniently normalized to After this, newly created and existing vacancies post wages.8 Next, unemployed workers see the menu of wages, and decide which wage, if any, to seek. The matching technology is the same as above. If the expected number of applicants is q, a worker is hired with probability /i(g) and a firm’s probability of hiring is r}(q). Finally, all employed workers and filled jobs produce f(k) units of output. If the firm cannot find a worker, its capital remains idle for the period. An unemployed worker receives UI equal to z. Unfilled vacancies and unemployed workers search again in the following period. We assume that a productive relationship between a worker and a firm never ends. Instead, we maintain a steady state population of unemployed workers by assuming the labor force Lt grows at rate 5 and all the 6Lt_i new workers are unemployed at the start of period t, with initial assets Ait — A0.9 Whenever you are going thought tough economic times, it makes sense to look for assistance online. We can give you instant pay day loans any day of the week, and you can apply right at www.get-instant-loans.com
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EFFICIENT UNEMPLOYMENT INSURANCE: A Dynamic Model Without Wealth Effects

A more interesting exercise, however, is to ask what level of UI maximizes workers’ expected utility, with entry, investment, and wage offers determined in equilibrium (rather than being directly chosen by the planner). To this end, we define optimal UI:

Definition 3 Let {kz,T,wZtT,qZiT} be an equilibrium with UI and taxes {z,t). Then, the policy (z°,t0) is optimal if it maximizes ii(qZ}T)u(A~-T-\-wZiT)-\-(l~ fi(qZ)T))u(A — T + z) subject to т = (1 — m(<Zz,t))z* Conjecture 1 Optimal UI (z°}r°) exists. For all и strictly concave, z° € {ze,z).

Intuitively, at the point of maximal output, a further increase in the UI leads to a second-order loss of net output, while it increases the income of unemployed workers and decreases the (after-tax) income of employed workers. This suggests workers will prefer the new, high UI “lottery”. Although we are unable to prove Conjecture 1, simulations support it.6 Also in our simulations it is always the case that an economy functioning at the level of Optimal UI has higher output than the economy with no UI. Therefore, contrary to conventional wisdom, increasing UI to moderate levels not only increases ex ante utility due to better risk-sharing, but also due to higher output. Payday loans represent a convenient borrowing tool if you do not feel comfortable contacting your family members or friends every time there’s a financial problem. We can offer a fast easy payday loan that no one has to know about: you are welcome to apply for it here easyloans-now.com
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A different way of expressing the intuition is to relate it to the efficiency results in search models with bargaining (e.g. Diamond, 1982; Sattinger, 1990; Hosios, 1990). In these models, if bargaining dictates that workers receive too small a fraction of the output they produce, unemployment is inefficiently low. In our model, risk-averse workers without UI prefer to receive a small fraction of output in order to reduce unemployment risk, and firms cater to these preferences by offering low wage jobs. This makes the level of frictional unemployment too low compared to the efficient level. More and more people find themselves dependent on their salaries more than they want to, so it’s not uncommon to need to buy something urgently without having the money for it. Check cash payday loans can be of great help in situations like that, so why not visit us at http://www.cash-loans-for-you.com/
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