Aspects of optimal unemployment insurance : Search, leisure, savings and capital market imperfections

Unemployment insurance is analysed in the optimal taxation framework. Benefits discourage search and thus raise unemployment. A perfect capital market model is developed and solved explicitly for a constant absolute risk aversion utility function. For ‘realistic’ parameter values low replacement rates (less than 50%) are optimal. If there is no lending or borrowing the optimal rates rise to about 75%. Alternative models also admit leisure as a good and the input to search; this reduces optimal replacement when the capital market is perfect. When it is nonexistent the optimal benefits depend on the value of leisure - rising as it falls. Alternatives to constant benefits conditional on continued unemployment are considered.     

Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle

This paper considers the optimal dividend problem with proportional reinsurance and capital injection for a large insurance portfolio. In particular, the reinsurance premium is assumed to be calculated via the variance principle instead of the expected value principle. Our objective is to maximize the expectation of the discounted dividend payments minus the discounted costs of capital injection. This optimization problem is studied in four cases depending on whether capital injection is allowed and whether there exist restrictions on dividend policies. In all cases, closed-form expressions for the value function and optimal dividend and reinsurance policies are obtained. From the results, we see that the optimal dividend distribution policy is of threshold type with a constant barrier, and that the optimal ceded proportion of risk exponentially decreases with the initial surplus and remains constant when the initial surplus exceeds the dividend barrier. Furthermore, we show that the optimization problem without capital injection is the limiting case of the one with capital injection when the proportional transaction cost goes to infinity.     

Replacement and the rental value of capital equipment subject to obsolescence

For a vintage model of capital equipment expressions for the implicit rental value and the optimal replacement policy are derived from the hypothesis of profit maximization. These will give unique solutions independent of product market conditions provided that two particular sequences converge to the same limit. The replacement rules of Terborgh, Smith, and Brems are shown to be special cases of this general model and also to depend on the particular convergence property of the sequences. The relationship of certain payoff period criteria to the optimal policy is also discussed.     

Optimal Two Sector Growth Models with Three Factors

The paper is devoted to construction of optimal trajectories in the model, which balances growth trends of investments in capital and labor efficiency. The model is constructed within the framework of classical approaches of the growth theory. It is based on three production factors: capital, educated labor and useful work. GDP level is described by a production function of the Cobb–Douglas type. The utility function of the growth process is given by an integral consumption index discounted on the infinite horizon. The optimal control problem is posed to balance investments in capital and labor efficiency. The problem is solved on the basis of dynamic programming principles. A novelty of the solution consists in constructing nonlinear stabilizers constructed on the feedback principle, which leads the system from any current position to a steady state. Growth and decline trends of the simulated trajectories are studied for all components included in the model.     

Multi-objective hedging model with the third central moment and the capital budget

The third central moment and the capital budget are two important factors in designing the optimal hedge strategy. This paper investigates the problem of futures hedging under the third central moment and the capital budget. Based on the multi-objective programming, a multi-objective hedging model with two important factors is proposed to manage this problem. Using the method of weighted sums, the multi-objective hedging model can be equivalently transformed into an ordinary single-objective programming. By solving the single-objective programming, we derive the optimal hedge ratio under the third central moment and the capital budget. Finally, an empirical example of hedging copper is given to illustrate the application of the proposed model. The results also show clearly the influence of the third central moment and the capital budget in the hedging decision.     

Vintage capital and the dynamics of the AK model

This paper analyzes the equilibrium dynamics of an AK-type endogenous growth model with vintage capital. The inclusion of vintage capital leads to oscillatory dynamics governed by replacement echoes, which additionally influence the intercept of the balanced growth path. These features, which are in sharp contrast to those from the standard AK model, can contribute to explaining the short-run deviations observed between investment and growth rates time series. To characterize the optimal solutions of the model we develop analytical and numerical methods that should be of interest for the general resolution of endogenous growth models with vintage capital.     

Preparing for catastrophic climate change

We study optimal adaptation to climate change when the harmful consequences of global warming are associated with uncertain occurrence of abrupt changes. The adaptation policy entails the accumulation of a particular sort of capital that will eliminate or reduce the catastrophic damage of an abrupt climate change when (and if) it occurs. The occurrence date is uncertain. The policy problem involves balancing the tradeoffs between the (certain) investment cost prior to occurrence and the benefit (in reduced damage) that will be realized after the (uncertain) occurrence date. For stationary economies the optimal adaptation capital converges monotonically to a steady state. In most cases, investment begins immediately. However, if the initial adaptation capital exceeds a pre-specified threshold level, which lies above the optimal steady state, investment is delayed while the capital stock decreases (due to depreciation) and commences only when it reaches this threshold level. For growing economies the optimal adaptation capital stock approaches the maximal economic level above which further accumulation is ineffective.     

On income fluctuations and capital gains

We consider the infinite time horizon problem of asymptotically maximizing the expected accumulated discounted utility in a one-good production economy. The available capital in a given period is given by the production of the previous period plus a random variable. The product of the discount and interest factors is either (1) greater than or (2) equal to one. Under (1) the optimal policy exists under certain conditions and always under (2). The optimal capital sequence almost surely goes to infinity. Under (1) with conditions on the utility one almost surely reaches a capital level above which the sequence is increasing.     

Spatial dynamics and convergence: The spatial AK model

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value function of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. Despite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.     

Macroeconomic stabilization in developing economies: Are optimal policies procyclical?

Many empirical studies provide evidence that macroeconomic policies as well as capital flows exhibit procyclical characteristics in developing economies. In particular Kaminsky et al. [2004. When it rains, it pours: Procyclical capital flows and macroeconomic policies. NBER Macroeconomics Annual, MIT Press] demonstrate that a large group of middle-income countries run contractionary policies and experience capital flight during times of recession. This paper investigates the role of international financial markets in explaining these macroeconomic policy and capital flow characteristics. An optimal fiscal and monetary policy problem is formulated and solved for a small-open economy that faces a country-specific interest rate spread in international financial markets. It is found that, in the presence of the country spread, optimal fiscal and monetary policies as well as capital flows are procyclical under a reasonable parametrization. Optimal policies and capital flows turn countercyclical in the absence of the country spread. This pattern is robust to a range of alternative model specifications.     

Vintage capital accumulation: Endogenous growth conditions

Optimal vintage capital accumulation is examined here under asymptotic endogenous growth conditions without input parametrization. It is shown that technological embodiment implies endogeneity of innovations. Vintange capital accumulation and time preference are shown to determine the endogenous rate of vintage capital depletion and the rate at which endogenous innovations occur. A vintage-truncation in capital utilization is shown to induce a time-truncation in the infinite-horizon vintage capital accumulation problem. Factor-augmenting technological change is not assumed a priori, but is shown to be a property of optimal vintage selection under balanced growth conditions.     

Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis*

Under certain weak assumptions such as free disposal and non-satiety, it is shown that the concavity of utility and of technology implies that the maximum value of the set of all attainable programmes is a concave function of the initial capital stocks. For time-independent problems, this implies that along an optimal path, as a capital stock is accumulated, its shadow price falls. The usefulness of the theorems is demonstrated in a number of examples, including Kemp's cake-eating problem and Forster's pollution-control problem.     

Optimal exporting of exhaustible resources with endogenous trade revenue: The case of a resource-scarce and capital-short economy

This paper discusses a dynamic trade problem of a resource-scarce and capital-short open economy. In this economy, exhaustible resources are traded for foreign capital. Different from previous research on similar topics, the models in this paper allows for endogenous export revenue. The optimal trade behavior of the economy is discussed here. The efficiency conditions for the optimal trading under various assumptions are derived. These conditions correspond to the noted Hotelling rules in a closed economy. Finally, policy implications of the results are presented.     

Adverse selection,asymmetric information,and foreign investment policies

This paper explores the welfare consequences of foreign investment taxation in a small open economy, based on the notion that the true productivity of imported capital may be unknown to policy-makers. It is shown that while asymmetric information between capital importers and the host government precludes the use of a productivity specific policy measure, an across-the-board policy suffers from the problem of adverse selection among capital imports of differential productivities. Conditions under which a reversal of the optimal foreign investment policy in the face of asymmetric information are examined.     

Optimal fiscal policy in the neoclassical growth model revisited

This paper studies optimal taxation in a version of the neoclassical growth model in which investment becomes productive within the period, thereby making the supply of capital elastic in the short run. Because taxing capital is distortionary in the short run, the government׳s ability/desire to raise revenues through capital income taxation in the initial period or when the economy is hit with a bad shock is greatly curtailed. Our timing assumption also leads to a tractable Ramsey problem without state-contingent debt, which can give rise to debt-financed budget deficits during recessions.     

Optimal income taxation with human capital accumulation and limited record keeping

This paper characterizes optimal income taxes in a dynamic economy where human capital is unobservable and the government is restricted to use taxes that depend only on current income. I show that unobservability of human capital tends to decrease the labor wedge, while the effect on the human capital wedge is uncertain. I also analyze the relationship between optimal taxes in economies with and without endogenous human capital and identify two qualitative reasons why the optimal tax codes will differ. I perform numerical simulations to calculate the quantitative relevance of endogenous human capital formation for optimal tax policy. I find that endogenous human capital lowers marginal tax rates by about 9% on average, as compared with a static model without human capital.     

Allocation of emission permits with leakage through capital markets

This paper analyses how tradable emission permits should be allocated to firms when capital is internationally mobile. When international environmental problems are attempted solved through uncoordinated policies between countries, it might be desirable for the home country to issue free emission permits in proportion to the use of capital in order to prevent leakage through international capital movements. The desirability of free emission permits will however be reduced if capital also can be employed in a domestic non-polluting sector. In this case, it may even be optimal to tax the use of capital in the polluting sector. It is also shown that it is always optimal to subsidise the use of capital in the polluting sector if the use of labour is taxed at an optimal rate. Finally, leakage does not affect the optimal domestic emission limit as long as appropriate capital subsidies and labour taxes are implementeed.     

Vintage capital,market structure and productivity in an evolutionary model of industry growth

This paper examines the effects of inter-firm variation in vintage equipment replacement policies on industry productivity and structure using an evolutionary model based on Nelson-Winter. Traditional industry productivity measures assume a graduated replacement policy with low variation across firms in the average age of the capital stock. This approach allows for inter-firm policy variation. The first part reviews the neoclassical treatment of vintage capital investment; the second part outlines an evolutionary model of vintage replacement in the context of industry growth; and the third part presents results of simulation experiments focused on the relationship between vintage replacement patterns and industry productivity growth. Findings suggest that inter-firm differences in vintage capital investment policies may account for significant shifts in the rates of industry productivity growth and changes in market structure.     

Royalty taxation under tax competition and profit shifting

Multinational corporations increasingly use royalty payments for intellectual property rights to shift profits globally. This not only threatens the tax base of countries worldwide but also affects the nature of tax competition. Against this background, our theoretical analysis suggests a surprising solution to the problem of curbing profit shifting without suffering major outflows of capital: a strictly positive withholding tax on royalty payments is both the Pareto-efficient solution under international coordination and the optimal unilateral response. If internal debt is sufficiently responsive, governments can even implement optimal targeting. Then, the royalty tax closes the profit-shifting channel, while all competition for mobile capital is relegated to internal-debt regulation. Our results question the ban on royalty taxes in double tax treaties and the EU Interest and Royalty Directive.     

Operating efficiency and output insensitive employment contracts for capital management

Summary This paper considers a problem in which an agent is hired to manage a capital investment and subsequently receives private information regarding the productivity of the capital investment. The capital manager must decide whether to invest capital supplied by the firm (the principal), or to divert these investment funds to perquisite consumption. If the manager decides to invest, the manager must then select the level of operating efficiency (productivity) of the capital investment, this latter choice being unobservable and constrained by the (maximal) productivity of the investment. In this setting we demonstrate that the optimal employment contract, from the perspective of the firm hiring the manager, is the contract whichminimizes the dependence of the manager's compensation on firm output. This contract pays the manager a fixed wage whenever output from the investment exceeds the wage and provides the manager with all of the projects rents whenever output falls below this level. Thus, we provide a setting in which fixed wage contracts are the optimal incentive contract even when agents are risk neutral and contracts can be costlessly written on future output.We would like to thank the participants in the Princeton Economics and Finance Workshop and the Ohio State University Finance Workshop for their comments on an earlier draft of this paper. The second author gratefully acknowledges the research support of the Georgia State College of Business Administration Research Council.