Public Debt,Productive Public Spending and Endogenous Growth

We analyse the effects of public debt in a basic endogenous growth model with productive public spending. We demonstrate that a discretionary policy in general violates the intertemporal government budget constraint along a balanced growth path. A balanced government budget gives a unique saddle point stable growth path. With a rule‐based policy, two saddle point stable balanced growth paths can occur, depending on the intertemporal elasticity of substitution of consumption and on the primary surplus policy. Higher debt goes along with smaller long‐run growth and we derive a condition such that a deficit‐financed increase in public spending raises the growth rate.     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

A simple endogenous growth model of financial intermediation with multiplicity and indeterminacy

This paper analyzes the role of financial intermediation in a simple endogenous growth model. The results suggest that multiple endogenous growth paths can exist in connection with various levels of financial development, due to the reciprocal externality between financial and real sectors. According to multiplicity, the growth effects of shocks on the technology of intermediation are opposite, depending on the balanced growth path. Furthermore, transitional dynamics is examined, and reveals that the high equilibrium is a saddle path, while the low-growth is locally stable. Therefore, the model presents local and global indeterminacy. These theoretical results support the large empirical literature on the relationship between financial development and growth which depicts conflicting impacts.     

Tariff,Growth, and Welfare

We develop a two‐country (Home and Foreign) by two‐good (consumption good and investment good) by one factor (capital) endogenous growth model with international knowledge spillover to study the relationship between an import tariff and economic growth and welfare. First, unlike the past literature, we do not need to make an assumption such that the growth rates between countries are identical in a balanced growth path (BGP). Second, we show that there exists a unique and saddle‐point BGP with both countries being incompletely specialized. Third, a higher import tariff on the consumption good in the domestic country may boost (reduce) the rate of economic growth when the foreign (domestic) country has an absolute advantage in the investment good. Finally, a rise in the tariff rate by one country may improve world welfare under some parameter spaces.     

Capital–labor substitution and balanced growth

This paper explores how different values of the elasticity of substitution between capital and labor (σ) impact on the balanced growth paths and growth potential of a country in exogenous growth models. The behavior of the system depends on the value of σ and the passage of σ through two critical values causes a qualitative change in the nature of the singular points and of its trajectories. The balanced growth path defined by a singular point in the form of a saddle-path exists and is locally stable if σ lies between two critical values.     

COMPETITIVE GROWTH IN A LIFE‐CYCLE MODEL: EXISTENCE AND DYNAMICS*

The dynamic behavior of the capital growth rate is analyzed using an overlapping‐generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise‐defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle‐point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.     

Endogenous Growth and Publicly Funded Knowledge Accumulation

We investigate a centrally planned, infinite horizon, single good economy in which new knowledge is generated in a separate R&D sector with government subsidy. The rate of growth of new ideas is assumed to be linear in the amount of labor devoted to R&D. Perpetual growth in per capita output and consumption is sustained by the spillover effects of knowledge creation. Using an isoelastic social welfare function and a general production function, the unique balanced growth path is characterized and the conditions for balanced growth to take place derived. In analyzing standard balanced growth, we demonstrate that so long as physical capital and knowledge grow at some arbitrarily constant rates along an optimal time path, the two rates must necessarily be equal. Using a Cobb–Douglas production function, the dynamic evolution of the economy is explicitly described in closed form for each state and control variables. In particular, it is shown that the economy either (i) attains the balanced growth path from the initial time, or (ii) converges monotonically to the balanced growth path. An asymptotic balanced growth path along which labor input in manufacturing tends to zero in the long run is ruled out by the tranversality condition on knowledge.     

Real purchasing power in the neoclassical monetary growth model

In the one sector neoclassical monetary growth model, the balanced growth path under perfect foresight is a saddle point. The paper demonstrates that this instability problem can be resolved by entering real purchasing power into the liquidity preference function as well as into the consumption function. This process allows an additional mechanism based on income effects in money demand by which a change in real balances can influence the growth path. Stability now depends critically on the size of such income effects given wealth effects from money demand. If stability is restored, the nature of the traditional non-neutrality of money must be qualified.     

Population dynamics and utilitarian criteria in the Lucas–Uzawa Model

This paper introduces population growth in the Uzawa–Lucas model, analyzing the implications of the choice of the welfare criterion on the model's outcome. Traditional growth theory assumes population growth to be exponential, but this is not a realistic assumption (see Brida and Accinelli, 2007). We model exogenous population change by a generic function of population size. We show that a unique non-trivial equilibrium exists and the economy converges towards it along a saddle path, independently of population dynamics. What is affected by the type of population dynamics is the dimension of the stable manifold, which can be one or two, and when the equilibrium is reached, which can happen in finite time or asymptotically. Moreover, we show that the choice of the utilitarian criterion will be irrelevant on the equilibrium of the model, if the steady state growth rate of population is null, as in the case of logistic population growth. Then, we show that a closed-form solution for the transitional dynamics of the economy (both in the case population dynamics is deterministic and stochastic) can be found for a certain parameter restriction.     

PROGRESSIVE TAXATION,ENDOGENOUS GROWTH,AND MACROECONOMIC (IN)STABILITY

In the context of a standard one‐sector model of endogenous growth, we show that the economy exhibits equilibrium indeterminacy and belief‐driven aggregate fluctuations under progressive taxation of income. When the tax schedule is regressive or flat, the economy's balanced growth path displays saddle‐path stability and equilibrium uniqueness. These results imply that in sharp contrast to a conventional automatic stabilizer, progressive income taxation may destabilize an endogenously growing macroeconomy by generating cyclical fluctuations driven by agents' self‐fulfilling expectations or sunspots.     

Autonomous demand and the warranted rate of growth

Unless equality is exogenously imposed between the rate of growthof autonomous demand and the warranted rate, a given rate ofgrowth of autonomous demand generates various 'short-period'warranted rates of growth, period by period. In a stable case,these 'short-period' warranted rates converge to a unique 'long-period'warranted rate, this being determined independently of the rateof growth of autonomous demand. Thus one has a non-steady pathof normal output growth. Different rates of growth of autonomousdemand engender, for one and the same configuration of normalincome distribution, different paths of normal output growth.Moreover, in a circulating-capital-only model with a given constantrate of growth of autonomous demand, different initial ratesof growth in aggregate demand also produce different paths ofnormal output growth. These results point to the importanceof effective demand in capital accumulation.     

A closed-form solution to the Ramsey model with logistic population growth

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb–Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.     

A dynamic analysis of an endogenous growth model with leisure

Summary. The main goal in this paper is to analyze an economic model of endogenous growth where human capital accumulation acts as the engine propelling economic activity. The added ingredient in our model is that agents derive utility from consumption and leisure, where leisure is defined as the amount of time devoted to those activities augmented by the level of education. Under regular conditions we show that there is a unique globally stable balanced growth path. We also provide a characterization of the behavior of our economic variables along the transition. Received: May 26, 1998; revised version: September 9, 1999     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Government spending and growth in second-best economies

This paper extends public spending-based growth theory along three directions: we assume a logistic trajectory for the ratio of government expenditure to aggregate income, self-limiting population change, and exogenous technological progress. By focusing on the choices of a benevolent social planner we find that, if the inverse of the intertemporal elasticity of substitution in consumption is sufficiently high, the ratio of consumption to private physical capital converges towards zero when time goes to infinity. Depending on the form of the underlying aggregate production function and on whether, for given production function, technological progress equals zero or a positive constant, our model may or may not yield an asymptotically balanced growth path (ABGP) equilibrium. When there is no exogenous technological progress, an equilibrium where population size, the ratio of government spending to aggregate income and the ratio of consumption to private physical capital are all constant does exist and the equilibrium is a saddle point. In case of positive technological progress numerical simulations show that the model still exhibits an ABGP equilibrium.     

Perfect foresight models and the dynamic instability problem from a higher viewpoint

Dynamic macroeconomic models incorporating perfect foresight expectations can display a dynamic instability of the saddle point type. So that unless the initial values happen to place the system on the stable arm of the saddle point, the economic variables will diverge ever more from the equilibrium. We consider the dynamic instability problem in a simple model of monetary dynamics which is non-linear and assumes adaptive expectations which are characterized by an expectations time lag. This model is shown to have a stable limit cycle. By considering perfect foresight as the limit as the expectations time lag tends to zero we are able to view the perfect foresight model from a dimension higher than that from which is it is normally viewed. We are thus able to see that the stable limit cycle continues to exist for the perfect foresight model as well. In this framework there is no longer a dynamic instability problem since whatever the intial values time paths are tending to the stable limit cycle.     

A simple dynastic economy with parental time investment in children’s patience

This article explores the dynamics of a general equilibrium when an individual’s rate of time preferences is endogenous in a dynastic competitive economy. We postulate that altruistic parents allocate time to make their children patient to improve their lifetime welfare. The paper shows multiplicity and instability of the competitive equilibrium. Local and global indeterminacy emerges due to complementarity between a balanced growth rate and parental time allocation. Indeterminacy implies income and growth disparity among generations. In contrast, a balanced growth path is unique and determinate in the corresponding social optimum. A unique social optimum introduces a potential policy instrument for stabilizing a cyclical competitive equilibrium.     

A model with endogenously determined cycles, discounting and growth

Summary. This article reexamines the role of consumption in growth and emphasises the external effects of aggregate consumption, viewed as consumption standards, as an additional impediment in the growth process. These external effects raise the productivity of the individuals and are positively related to their valuation of the future. Conditions are established under which this results in a marginal value of wealth that is an increasing function of consumption. This brings new types of multiple steady states, local indeterminacies and cyclical motions. Imposing extra homogeneity restrictions, balanced growth solutions with endogenous impatience emerge. The possibility of multiple convergent paths is univocally related to endogenous discount effects. A comparison with a benchmark planning economy indicates an excessive value for the rate of time preference and emphasises its insufficient adaptation to future utility in a stationary setting. Discrepancies along the transition path that rest on endogenous impatience versus fixed discount appear in a non-stationary environment when the competitive balanced growth solution is indeterminate. Received: May 5, 1996; revised version: May 19, 1997     

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.     

Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth

The “linearity critique” of endogenous growth models is presented in a general context of an arbitrary growth model and reassessed. It is argued that presence of linearities is not a valid criterion for rejecting growth models. Existence of exponential/geometrical steady-state growth (i.e. of a balanced growth path with strictly positive growth rates) necessarily requires some knife-edge condition which is not satisfied by typical parameter values. Hence, balanced growth paths are fragile and sensitive to smallest disturbances in parameter values. Adding higher order differential/difference equations to a model does not change the knife-edge character of steady-state growth.