Investments into education—Doing as the parents did

Empirical evidence suggests that parents with higher levels of education generally attach a higher importance to the education of their children. This implies an intergenerational chain transmitting the attitude towards the formation of human capital from one generation to the next. We incorporate this intergenerational chain into an OLG-model with endogenous human capital formation. In absence of any state intervention such an economy might be characterized by multiple steady states with low or high human capital levels. There are also steady states where the population is permanently divided into different groups with differing human capital and welfare levels. Compulsory schooling is needed to overcome steady states with low human capital and welfare levels. Tax financed education subsidies can lead to further pareto-improvements.     

Two‐level CES Production Technology in the Solow and Diamond Growth Models*

The two‐level CES aggregate production function—that nests a CES into another CES function—has recently been used extensively in theoretical and empirical applications of macroeconomics. We examine the theoretical properties of this production technology and establish existence and stability conditions of steady states under the Solow and Diamond growth models. It is shown that in the Solow model the sufficient condition for a steady state is fulfilled for a wide range of substitution parameter values. This is in sharp contrast with the two‐factor Solow model, where only an elasticity of substitution equal to one is sufficient to guarantee the existence of a steady state. In the Diamond model, multiple equilibria can occur when the aggregate elasticity of substitution is lower than the capital share. Moreover, it is shown that for high initial levels of capital and factor substitutability, the effect of a further increase in a substitution parameter on the steady state depends on capital–skill complementarity.     

Capital Flight, North-South Lending, and Stages of Economic Development

We present a two-country OLG economy in which international capital mobility exists in the presence of moral hazard in financial contracts. The difference in the extent of asymmetric information is a source of capital movement and capital flows from the South to the North. Even though there exists a unique steady state under autarky, multiple locally stable steady states may emerge in a world economy with an integrated capital market. However, the integration may drive the South down to further impoverishment. The South's government therefore should take into account seriously the timing of capital market liberalization as a conduit of economic development.     

Human capital investment,credentialing, and wage differentials

This study considers how individuals determine at what ratio they will invest in two different types of education. The first type contributes to the development of labor skills, while the other does not. We refer to the former as human capital investment and the latter as unproductive investment, which improves test scores but has no beneficial effect on students' human capital. We formulate an overlapping‐generations economy in which the rich and poor households invest in both types of education. We find that the ratio of human capital investment to unproductive investment is lower in the economy with medium size of the wage differentials. In a dynamic analysis, we identify two patterns of stable steady states for the dynamics of the wage differentials, namely, no‐inequality and high‐inequality steady states. Further, we show that a rapid increase in the level of skill‐biased technology may cause a switch from a steady state with no‐inequality to one with high inequality. This causes at least a temporary increase in the ratio of unproductive investment during the transition to the new steady state.     

A NOTE ON “A ONE‐SECTOR NEOCLASSICAL GROWTH MODEL WITH ENDOGENOUS RETIREMENT”: EXISTENCE OF MULTIPLE STEADY STATES*

This note extends Matsuyama's 0–1 endogenous retirement choice model to the framework with continuous endogenous retirement choice to study the consumption‐saving decision and capital accumulation in an overlapping generation model. The conditions for the existence of multiple steady states have been derived. In contrast to the 0 or 1 labour choice, the partial retirement may be a stable steady state under the continuous endogenous retirement choice in the second period. And this implies that partial retirement may be a stable optimal choice. Also, we find that the retirement choice depends on the initial capital stock when there are multiple steady states.     

The Budget Deficit, Public Debt, and Endogenous Growth

This paper analyzes the effects of public debt on endogenous growth in an overlapping generations model. The government fixes the budget deficit ratio. If the deficit ratio stays below a critical level, then there are two steady states where capital, output, and public debt grow at the same constant rate. An increase in the deficit ratio reduces the growth rate. If the deficit ratio exceeds the critical level, then there is no steady state. Capital growth declines continuously, and capital is driven down to zero in finite time.     

Management Ability, Long-run Growth, and Poverty Traps

This study establishes an R&D-based growth model that includes the functional difference between labor and human capital in the production of goods. In our analysis, human capital is used by the managers in the manufacturing process. Such an allocation of human capital yields three possible steady states: endogenous growth, poverty traps, and multiple equilibria. Economies are sorted into these steady states according to the endowments of labor, human capital, and knowledge. Thus, the obtained steady states explain some economic growth patterns, such as polarization and leapfrogging of economies.     

Multiplicity and stagnation under the Romer model with increasing returns of R&D

This study develops a simple growth model to explain stagnation and non-simple growth patterns by using increasing returns of R&D efficiency. The study adopts a type of the lab-equipment model, namely, the Romer model, where goods are used as R&D input. Here, we assume capital, or durable goods, as the R&D input factor, and R&D efficiency is assumed to be variable. This arrangement yields three steady states, namely: no-growth, low-growth, and high-growth steady states. These trajectories are jumpable. Accordingly, global indeterminacy is obtained. By uniting the numerical analysis, we obtain that all steady states are saddle stable. However, when the increasing R&D efficiency is small, the path converging to a high-growth-rate steady state shows local indeterminacy.     

Status-Seeking, Catching-Up, and Comparative Statics in a Dynamic Heckscher–Ohlin Model

This paper examines a two‐country dynamic general equilibrium model with status‐seeking agents. We show that the introduction of status‐seeking behavior brings about new properties in equilibrium dynamics. While there exists a continuum of steady states in the standard dynamic models, the present framework demonstrates that, under some conditions, there uniquely exists an incompletely specialized steady state, which is locally saddle‐point stable. Therefore, catching‐up and overtaking phenomena seen in economic development can be explained, and comparative statics analysis also is made possible. Our comparative statics analysis illustrates, for example, that trade pattern is determined in the Heckscher–Ohlin manner; the patient country acts just like a capital abundant one to export the capital‐intensive good. Furthermore, as distinct from the existing literature, the present study shows that the existence of an incompletely specialized steady state can be ensured even if the two countries conduct different policies.     

Economic Growth with Foreign Capital

In growth theory, foreign investment places a small open economy in the international steady state. In applied growth theory, foreign investment is assumed to shift technology. The present growth model separates foreign from domestic capital and develops the steady state where both capital/labor ratios are stationary. A capital scarce country would attract foreign investment and may arrive at a steady state with perpetual foreign investment. Such a steady state foreign investment host is characterized by low saving and high labor growth rates, and source countries the opposite. Incomplete convergence characterizes economic growth with foreign capital.     

The taxation of capital returns in overlapping generations models

This paper shows that in the Diamond (1965) overlapping generations economy with production and capital savings, there is a period-by-period balanced fiscal policy supporting a steady state allocation that Pareto-improves upon the laissez-faire competitive equilibrium steady state (whether dynamically inefficient or efficient) without resorting to intergenerational transfers. The policy consists of taxing linearly (or subsidizing, in the dynamically efficient case) the returns to capital, while balancing the budget period by period through a lump-sum transfer (or tax, respectively) in second period. This intervention grants every generation the highest steady state utility attainable through markets (i.e. remunerating factors by their marginal productivities and without transfers) which under laissez-faire is not a competitive equilibrium outcome. A transition from the competitive equilibrium steady state to this other steady state is also Pareto-improving when the former is dynamically inefficient. The result disentangles from redistributive considerations the impact of the taxation of capital returns on steady state welfare, and thus provides a rationale for the taxation of capital returns that is based on efficiency considerations and not on redistributive goals.     

Environmental Quality,Public Debt and Economic Development

This article analyzes the consequences on capital accumulation and environmental quality of environmental policies financed by public debt. A public sector of pollution abatement is financed by a tax or by public debt. We show that if the initial capital stock is high enough, the economy monotonically converges to a long-run steady state. On the contrary, when the initial capital stock is low, the economy is relegated to an environmental poverty trap. We also explore the implications of public policies on the trap and on the long-run stable steady state. In particular, we find that government should decrease debt and increase pollution abatement to promote capital accumulation and environmental quality at the stable long-run steady state. Finally, a welfare analysis shows that there exists a level of public debt that allows a long run steady state to be optimal.     

Implementing Steady State Efficiency in Overlapping Generations Economies with Environmental Externalities

We consider in this paper overlapping generations economies with pollution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that the dynamical inefficiency of a competitive equilibrium steady state with capital–labor ratio exceeding the golden rule ratio still holds. Moreover, the range of dynamically efficient steady state capital ratios increases with the effectiveness of the environment maintenance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the transition to the social planner's steady state.     

Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.This paper is dedicated to Professor Mukul Majumdar on his 60th birthday. His research with various co-authors in the late 70s and the 80s pioneered innovative techniques for the analysis of nonconvex dynamic optimization models – both deterministic and stochastic. Roy considers himself particularly fortunate for having had the opportunity to learn economic theory and mathematical economics from Professor Majumdar. This paper has benefited from helpful comments and suggestions by an anonymous referee. Financial support from the 21st Century COE Program at GSE and RIEB, Kobe University, is gratefully acknowledged.     

Inflationary Finance, Capital Controls, and Currency Substitution

This paper studies currency substitution in an environment where agents' inflation tax-evasive demand for foreign money is balanced by the concern for the possibility that the government may impose economy-wide capital controls under which foreign currency transactions are costly. Under the assumption of endogenous beliefs, the results show a persistent demand for foreign money despite efforts by the government to reduce inflation. In addition, the economy can exhibit multiple, Pareto-ranked steady states with different levels of currency substitution. The stability analysis suggests that the economy converges to the inferior steady state, on the "wrong side" of the Laffer curve.     

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.     

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.     

Rich and Poor Countries in Neoclassical Trade and Growth

A neoclassical growth model provides an explanation for a 'poverty trap', 'club convergence', or 'twin peaks', in terms of specialisation and international trade. The model has many countries with identical linearly homogeneous technologies for producing three goods using capital and labour. With diverse initial endowments, initial equilibrium has unequal factor prices and two diversification cones. With savings out of wages, following Galor (1996), there may easily be multiple steady states. Poor countries converge to a low steady state while rich countries converge to a high one, even though all share identical technological and behavioural parameters.     

Is fiscal austerity really self-defeating?

This paper analyzes local and global equilibrium dynamics in an optimizing endogenous growth model under expenditure-based fiscal austerity feedback policies expressed relative to the private capital stock—prescribing spending cuts in reaction to public debt accumulation. Because the present value of equilibrium primary surpluses turns to be a nonlinear function of debt, two steady state equilibria are shown to emerge, one exhibiting low debt and high growth, one exhibiting high debt and low growth. Local analysis reveals that the low-debt/high-growth steady state is saddle-path stable while the high-debt/low-growth steady state is unstable—the latter thus indicating the possibility of self-defeating austerity, characterized by off-equilibrium upward spirals in debt because of persistent policy-induced adverse effects on growth dividends and fiscal revenues. However, when global nonlinear dynamics are taken into account, it is demonstrated that the two steady states are endogenously connected. In particular, global analysis reveals that even if the high-debt/low-growth steady state is locally unstable, there exists a unique and possibly nonmonotonic saddle connection making the economy converge to the low-debt/high-growth steady state. The existence of the saddle connection guarantees global determinacy of perfect foresight equilibrium should the high-debt/low-growth steady state be a node, ruling out multiple explosive paths incompatible with the government's intertemporal budget constraint and the private agents' transversality condition. The foregoing results are robust with respect to the adoption of an output-based—rather than a capital-based—policy function as long as the rule is nonlinear and sufficiently reactive to debt changes.     

FOREIGN CAPITAL AND ECONOMIC GROWTH

This paper examines the economic implications of institutional arrangements by which foreign investors are required to reinvest a certain percentage of their capital within the host country. Our analysis shows that foreign capital inflow can produce long-lasting economic benefits to the host country only when the foreign capital reinvestment rate is sufficiently greater than the host country's saving rate. In this case, the economy evolves into a unique steady state equilibrium, which is also asymptotically stable. The paper also presents several comparative static results regarding the responses of steady state capital-labour ratio and the proportion of foreign capital in total capital to changes in the population growth rate, the rate of capital depreciation, the host country's saving rate and the foreign capital reinvestment rate.