OPTIMAL CAPITAL TAXES FOR PUBLIC GOOD PROVISION*

This paper constructs a general equilibrium trade model of a small open economy that produces many traded private goods and one non-traded public consumption good. Trade in goods is free, but the country taxes the internationally mobile capital to finance the provision of the public good. Within this framework, the paper identifies the conditions under which the optimal policy on the internationally mobile capital calls for a tax. Under the assumptions that (i) the welfare function is concave with respect to the tax rate, and (ii) the net revenue-maximizing capital tax rate is positive, it is shown that the marginal cost of the public good always understates its social marginal cost.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

Optimal climate and fiscal policy in an OLG economy

This paper develops a climate–economy model to study the joint design of optimal climate and fiscal policies in economies with overlapping generations (OLGs). I demonstrate how capital taxation, if optimal, drives a wedge between the market costs of carbon (the net present value of marginal damages using the market interest rate) and the Pigouvian tax (the net present value of marginal damages using the consumption discount rate of successive OLGs). In contrast to deterministic infinitely lived representative agent models, at the optimum, the capital income tax is positive, the carbon price equals the market costs of carbon but it falls short of the Pigouvian tax when (i) preferences are not separable over consumption and leisure; and (ii) labor income taxes cannot be age-dependent. I also show that restrictions on climate change policy provide a novel rationale for positive capital income taxes.     

Capital income taxation,depreciation allowances and economic growth: A perfect-foresight general equilibrium model

Conclusions The results indicated in Table 1 show that incomplete depreciation allowances reinforce the distortions in the equilibrium growth path brought about by an ideal capital income tax. A reduction in the deductible share of economic depreciation, like an increase in the tax rate, raises the current level of consumption, but reduces the steady state levels of consumption and capital per efficiency unit of labour.The reason for these distortions is that the tax law is able to drive wedges both between the rate of time preference and the market rate of interest, and between the latter and the marginal productivity of capital. The first wedge is created through capital income taxation as such and its size is directly related to the tax rate. The second wedge is created by the incomplete deductibility of depreciation. Its size is directly related to the tax rate and inversely to the deductible share of depreciation. For the distortion in the growth path of the economy it is the sum of the two wedges that counts. Therefore it is plausible that incomplete depreciation allowances reinforce the effects of capital income taxation.Knowing the determinants of the two wedges one can easily derive the influence of a tax reform on the marginal productivity of capital, the market rate of interest and the rate of time preference (cf. Table 2). In the short run, the system of these three interest rates is anchored by the marginal productivity of capital, and hence any measure that widens a wedge is translated into a reduction in the rate or those rates below the wedge. In the long run the system is anchored by the rate of time preference and an increase in the width of a wedge is translated into an increase in those rates or that rate above this wedge.The paper was written in association with the Sonderforschungsbereich 5 (Staatliche Allokationspolitik im marktwirtschaftlichen System).     

Optimal Taxation in Life-Cycle Economies

We use a very standard life-cycle growth model, in which individuals have a labor-leisure choice in each period of their lives, to prove that an optimizing government will almost always find it optimal to tax or subsidize interest income. The intuition for our result is straightforward. In a life-cycle model the individual's optimal consumption-work plan is almost never constant and an optimizing government almost always taxes consumption goods and labor earnings at different rates over an individual's lifetime. One way to achieve this goal is to use capital and labor income taxes that vary with age. If tax rates cannot be conditioned on age, a nonzero tax on capital income is also optimal, as it can (imperfectly) mimic age-conditioned consumption and labor income tax rates. Journal of Economic Literature Classification Numbers: E62, H21.     

Legal Institutions, Sectoral Heterogeneity, and Economic Development

Poor countries have lower PPP-adjusted investment rates and face higher relative prices of investment goods. It has been suggested that this happens either because these countries have a relatively lower TFP in industries producing capital goods or because they are subject to greater investment distortions. This paper provides a micro-foundation for the cross-country dispersion in investment distortions. We first document that firms producing capital goods face a higher level of idiosyncratic risk than their counterparts producing consumption goods. In a model of capital accumulation where the protection of investors' rights is incomplete, this difference in risk induces a wedge between the returns on investment in the two sectors. The wedge is bigger, the poorer the investor protection. In turn, this implies that countries endowed with weaker institutions face higher relative prices of investment goods, invest a lower fraction of their income, and end up being poorer. We find that our mechanism may be quantitatively important.     

Collateral secured loans in a monetary economy

This paper presents a microfounded model of money where durable assets serve as a guarantee to repay consumption loans. We study a steady state equilibrium where money and credit coexist. In such an equilibrium, a larger investment in durable capital relaxes the borrowing constraint faced by consumers. We show that the occurrence of over-investment and the behavior of capital accumulation depend on the rate of inflation, the relative risk aversion of agents and the marginal productivity of the capital goods.     

On the emergence of competitive equilibrium growth cycles

A basic discrete-time heterogeneous capital goods competitive environment is considered, its potential for displaying steady growth solutions analyzed and the properties of the latter characterized. A first composite good may be used for consumption or investment on a one-to-one basis, while a second good is only used for accumulation, solely capital inputs being part of the production process. This framework is first considered from the allocative standpoint through the derivation of the frontier of the production possibility set. Having defined the perfect foresight competitive equilibrium that also describes a Pareto optimum over time, attention is then given to the potential for unbounded steady growth solutions. Under interiority, summability, and expansivity restrictions, there is a unique optimal steady growth rate. For unitary depreciation rates of both capital goods, locally there exists a unique convergent sequence to this steady growth solution that exhibits a saddlepoint structure. However, as soon as one of the depreciation rates of the capital goods is non-unitary and the profit share accruing to the first capital stock is greater in the second pure accumulation industry than in the first composite good industry, the steady growth solution shows a loss of stability, and competitive equilibrium growth cycles emerge through the occurrence of a flip bifurcation in its neighborhood. This is the first optimal cycles result based upon a production set that does not explicitly incorporate any exogenously determined primary labor input in its definition.     

Time-consistent taxation in a dynastic family model with human and physical capital and a balanced government budget

Abstract .  This paper analyzes optimal, time consistent taxation in a dynastic family model with human and physical capital and with a balanced government budget. When tax revenue is used for publicly provided consumption or lump-sum transfers, leisure would be higher than its social optimum. Pareto optimal taxation requires taxing capital income more heavily than labour income and subsidizing investment at the same rate of the tax. Also, it requires either subsidizing labour at the same rate as a consumption tax or subsidizing consumption at the same rate as a labour income tax, and hence it is not a practical guide to policy. Further, a consumption tax, or equivalently a uniform income tax with investment subsidies at the same rate, can be improved on by taxing capital income more heavily than labour income.     

The Optimal Timing of Adoption of a Green Technology

We study the optimal timing of adoption of a cleaner technology and its effects on the rate of growth of an economy in the context of an AK endogenous growth model. We show that the results depend upon the behavior of the marginal utility of environmental quality with respect to consumption. When it is increasing, we derive the capital level at the optimal timing of adoption. We show that this capital threshold is independent of the initial conditions on the stock of capital, implying that capital-poor countries tend to take longer to adopt. Also, country-specific characteristics, as the existence of high barriers to adoption, may lead to different capital thresholds for different countries. If the marginal utility of environmental quality decreases with consumption, a country should never delay adoption; the optimal policy is either to adopt immediately or, if adoption costs are “too high”, to never adopt. The policy implications of these results are discussed in the context of the international debate surrounding the environmental political agenda.      

Optimal labor income taxation in a two-sector dynamic general equilibrium model

This paper presents a new approach to the two-sector optimal taxation problem. We derive the optimal labor income tax rate which depends on factor intensity across sectors. It is the labor intensity that determines the initial wage rate, and therefore the optimal labor tax rate. We show that an increase in the initial relative price of consumption goods decreases the optimal tax rate on labor income in the case that the consumption goods sector is capital-intensive while it increases the optimal tax rate on labor income in the case that the investment goods sector is capital-intensive.     

The Transfer Problem and Real Exchange Rate Overshooting in Financial Crises: The Role of the Debt Servicing Multiplier*

We develop a real model of exchange rate overshooting due to a debt servicing multiplier. Borrowers of foreign capital are bound by noncontingent contracts to pay the world rate of return following an adverse shock. This is onerous, since the marginal product of capital is less than the world rate of return and the shock causes some capital to become extra‐marginal. If the resultant debt servicing shortfall is met by taxes on workers, this reduces their demand for nontradable goods, which feeds back onto their wage, reducing their demand for nontradable goods, etc. In the short run, when extra‐marginal projects are “stuck” in the economy, the real exchange rate can overshoot. This mechanism may help to explain overshooting of exchange rates in the 1997 Asian financial crisis.     

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.     

Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households

We prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two-sector model with infinitely lived heterogeneous agents. The most patient agent holds all the capital in this solution. We also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock, then the aggregate capital stock eventually is monotonic and converges to the steady state stock. If the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions. Periodic equilibria are shown to exist under weaker hypotheses. Journal of Economic Literature Classification Numbers: D52, D90, E13.     

Risky human capital and deferred capital income taxation

We study the structure of optimal wedges and capital taxes in a dynamic Mirrlees economy with endogenous distribution of skills. Human capital is a private, stochastic state variable that drives the skill process of each individual. Building on the findings of the labor literature, we construct a tractable life-cycle model of human capital evolution with risky investment and stochastic depreciation. In this setting, we demonstrate the optimality of (a) a human capital premium, i.e., an excess return on human capital relative to physical capital, (b) a large intertemporal wedge early in the life-cycle, and (c) a non-zero intratemporal wedge even at the top of the skill distribution at all dates except the last date in the life-cycle. The main implication for the structure of optimal linear capital taxes is the necessity of deferred taxation of physical capital. The average marginal tax rate on physical capital held in every period is zero in present value. However, expected capital tax payments do not equal zero in every period. Necessarily, agents face negative expected capital tax payments early in the life-cycle and positive expected capital tax payments late in the life-cycle.     

金融发展的福利收益和"门槛效应"--一个动态最优增长分析

文章采用无限期界的动态最优控制方法,给出一个最优经济增长模型,讨论金融发展对消费福利的影响。结论显示,金融发展通过提升要素生产率和金融效率产生消费与财富上的“增长率收益”,但金融效率提升和金融发展成本也降低消费-财富比,引起短期消费的下跳。因此,金融发展促进福利收益,但存在“门槛效应”。门槛高度取决于现有技术水平(要素生产率)、居民消费的时间偏好、人口增长率等。这些方面的差异导致各国在通过金融发展促进福利增长上后果不一。这对一国选择金融发展政策具有指导作用。     

Dynamic contracting with persistent shocks

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound—immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.     

Imperfect Tax Compliance and the Optimal Provision of Public Goods

Our aim in this paper is to investigate whether the presence of imperfect income tax compliance affects the optimal provision of public goods within a framework in which public expenditure is financed by a general income tax that also accomplishes redistributive goals. We first derive the income tax structure, and then a generalized Samuelson rule. We argue that, under imperfect income tax compliance, it is desirable to distort public–good supply downwards, in the sense that the sum of marginal rates of substitution between public and private consumption must exceed their marginal rate of transformation.     

Neoclassical Growth, Manufacturing Agglomeration, and Terms of Trade

This study reverses the prediction of geography and growth models that trade integration may cause income divergence. Moreover, a new dynamic welfare gain of trade openness is identified. These results are obtained from embedding a new economic geography model into a neoclassical growth model. Starting from symmetric countries, a country that accumulates more capital than the other increases its home market size, improves its terms of trade, and lowers its relative consumption price index, because trade costs drive a wedge in between relative producer and consumption price indices. Both effects in turn tend to increase its marginal revenue product of capital relative to the other country (divergence forces), while factor substitution diminishes its marginal revenue product of capital (convergence force). Reducing trade costs decreases the wedge and weakens the divergence forces, while the convergence force is unaffected. Hence, divergence is more likely with higher rather than lower trade costs.     

The Mordukhovich Normal Cone and the Foundations of Welfare Economics

The statement that Pareto optimal allocations require the equalization of marginal rates of substitution, or in an economy with public goods, require the equalization of the aggregate of the marginal rates in consumption to those in production, is formalized through the use of the Mordukhovich normal cone. Since this cone is strictly contained, in general, in the Clarke normal cone, the results generalize earlier work of Khan and Vohra, Quinzii, Yun, and Cornet. The results are an application of Mordukhovich's 1980 theorem on necessary conditions for optimality in constrained optimization problems involving functions that are not necessarily differentiable or quasi-concave. As such, the results suggest a distinction between the mathematical programming approach to the "second welfare theorem," as in the work of Hicks, Lange, and Samuelson, and that based on the separation of sets, as pioneered by Arrow and Debreu.