Saddle Path Research Articles

Nonrenewable resource use sustainability and public debt

AbstractThe sustainability of resource use and the management of public finances are both long‐run issues that are linked to each other through savings decisions. To study them conjointly, this paper introduces a public debt stabilization constraint in an overlapping generation model in which nonrenewable resources constitute a necessary input in the production function and belong to agents. It shows that stabilization of public debt at a high level (as share of capital) may prevent the existence of a sustainable development path, that is, a path on which per capita consumption is not decreasing. Public debt thus appears as a threat to sustainable development. It also shows that higher public debt‐to‐capital ratios (and public expenditures‐to‐capital ones) are associated with lower growth. Two transmission channels are identified. As usual, public debt crowds out capital accumulation. In addition, public debt tends to increase resource use which reduces the rate of growth. We also provide a numerical analysis of the dynamics that shows that the economy is characterized by saddle path stability. Finally, we show that the public debt‐to‐capital ratio may be calibrated to implement the social planner optimal allocation according to which the growth rate is increasing in the degree of patience.

Unstable diffusion in social networks

How and to what extent will new activities spread through social ties? To answer this question, we present an analytical framework that allows us to describe the diffusion dynamics on complex networks more accurately than the conventional mean-field approach. Based on two classes of network games, we find that the spread of multiple activities is expressed as a saddle path, and thus, inherently unstable. In particular, when the two activities are sufficiently substitutable, either of them will dominate the other by chance even if they are equally attractive ex ante. We argue that, in environments where such symmetry-breaking occurs, any average-based approximation method may not correctly capture the Nash equilibrium — the steady state of an actual diffusion process.

Diffusion dynamics of competing information on networks.

Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problems, it remains an open question what dynamics emerge in the diffusion process when individuals face multiple (and possibly incompatible) information sources. Here, we develop a microfounded general threshold model that enables us to analyze the collective dynamics of individual behavior in the propagation of multiple information sources. The analysis reveals that the virality of competing information sources is fundamentally indeterminate. When individuals maximize coordination with neighbors, the diffusion process is described as a saddle path, thereby leading to unpredictable symmetry breaking. When individuals' choices are irreversible, there is a continuum of stable equilibria where a certain degree of social polarization takes place by chance.

Intra-industry trade, involuntary unemployment and macroeconomic stability

We introduce taste for variety in a one-sector model of differentiated products with productive labor externalities, considering two OLG countries, one with wage rigidity and the other with full employment. After opening the borders to capital mobility and intra-industry trade, steady state output and real wages improve in the full employment country and the saddle path stability, characterizing this country under autarky, will prevail in the globalized world if this economy is big enough. Unemployment increases in the country with wage rigidity and, for intermediate plausible values of both the current propensity to consume and of the labor externality, indeterminacy, which emerges in the rigid wage economy in autarky, will be exported to the world if this country is relatively big. Finally, we show that globalization leads to the appearance of stable deterministic cycles in activity, employment and the trade account, both through flip and Hopf bifurcations, when the world steady state is locally determinate, for empirically plausible low degrees of labor externalities. This implies that trade cycles occur in the absence of shocks to fundamentals, and even without uncertainty in expectations.

Environmental regulation policy, corporate pollution control and economic growth effect: Evidence from China

This paper constructs a theoretical framework including pollution accumulation that describes the corporate pollution treatment mechanism, and uses the shooting method to find the equilibrium solution on saddle path of the neoclassical model. It simulates the effects of pollution reduction and economic growth under the three scenarios of “no environmental regulation policy”, “with environmental tax policy”, and “with a combination of environmental tax policy and subsidy policy for pollution control”. The results show that in the absence of any environmental regulation policy, firms will not incorporate the social cost of pollution emissions into their own production cost and have no incentive for pollution control. When implementing environmental tax policy, firms will be motivated to invest more into pollution control because the cost of penalties on firms rapidly increases as environmental tax rate rises and the negative impact of pollution on business production continues to deepen, and the marginal return on energy input begins to fall. Compared with sole implementing environmental tax policy only, a combination of environmental tax policy and subsidy policy for pollution control can further stimulate firms’ incentives, which achieves a virtuous cycle between output growth, pollution reduction and corporate treatment, reaching effects of pollution reduction and economic growth.

PHYSICAL CAPITAL, HUMAN CAPITAL, AND THE HEALTH EFFECTS OF POLLUTION IN AN OLG MODEL

In a standard overlapping generations model, we show how the health effects of pollution impact the balanced-growth path (BGP) and the transition dynamics of the economy. The key driver is the differential between physical and human capital accumulation. The differential occurs because pollution alters the incentives to save and to invest in education via reductions in longevity and alters the effectiveness of education expenditures via impaired cognitive learning. Two predictions of the model are noteworthy. The first prediction is the existence of two stable BGPs with a separating saddle path. One BGP is desirable featuring high economic growth and low pollution, whereas the other should be avoided because it is associated with low economic growth and high pollution. The second prediction is that economic and environmental cycles may emerge, implying inequality between generations. These theoretical results are supported by empirical evidence and imply a role for government to steer the economy toward the desirable BGP and eliminate the cycles.

The Effects of Biased Technical Progress with Endogenous Growth on Factor Shares

Based on the CES model by Arrow et al., this paper incorporates the hypothesis of induced innovation, takes household and firm behavior as subjects, and analyzes the effects of biased technical progress on factor shares with endogenous growth. The results show that, if substitution elasticity s more than 1, the factor-augmenting model generates endogenous growth; if saving rate is constant, and technical progress s Harrod neutral, there is a saddle path, capital share remains constant and technical progress is biased to capital; if savings rate is not a constant, nor technical progress Harrod neutral, then there is still a saddle path, but equilibrium point is half equilibrium point, and the bias turns towards labor. It is also found that when innovation possibility frontier is symmetric, capital share is less than 1/2, and long run factor shares are consistent with the theory.

Unstable diffusion in social networks

How and to what extent will new activities spread through social ties? Here, we develop a more sophisticated framework than the standard mean-field approach to describe the diffusion dynamics of multiple activities on complex networks. We show that the diffusion of multiple activities follows a saddle path and can be highly unstable. In particular, when the two activities are sufficiently substitutable, either of them would dominate the other by chance even if they are equally attractive ex ante. When such symmetry-breaking occurs, any average-based approach cannot correctly calculate the Nash equilibrium - the steady state of an actual diffusion process.

Intra-Industry Trade, Involuntary Unemployment and Macroeconomic Stability

We study the impact of intra-industry trade and capital mobility on steady state welfare and on the stability properties of two countries with identical technologies and preferences. We consider a two-factor overlapping generations model, featuring one-sector of differentiated goods with taste for variety. There is imperfect competition in the output market and increasing returns to scale in production (fixed costs and externalities). In one country there is full employment and saddle path stability in autarky, whereas in the other there are efficiency wages, and the autarkic equilibrium may be locally indeterminate. After opening the borders, the rigid wage country may export indeterminacy to the full employment country, particularly if it is big enough. In contrast, when the full employment country is sufficiently big, local indeterminacy, and therefore expectations driven fluctuations may be eliminated in the world. In any case, stochastic and deterministic fluctuations (associated with local indeterminacy and bifurcations) are possible with smaller externalities, whatever the relative size of the two countries. Steady state welfare improves in the full employment country with free trade and capital mobility, while unemployment increases in the country with labor market rigidities, reducing welfare. We also find that taste for variety (and therefore intra-industry trade), reduces the likelihood of local indeterminacy, but leads to flip bifurcations under more plausible values of the model parameters.

Pollution permits, green taxes, and the environmental poverty trap

AbstractWe compare the steady states and transition dynamics under pollution permits and under green taxes in an overlapping generations model with endogenous longevity. Multiple steady states can emerge under pollution permits. One nontrivial steady state is an environmental poverty trap (EPT). This steady state is characterized by low capital and high pollution. An economy operating in the neighborhood will gravitate toward this steady state in the long run. The other nontrivial steady state featuring high capital and low pollution is desirable. A saddle path may lead to this desirable steady state. In contrast, the steady state under green taxes is unique and locally stable. We also design policies that prevent an economy from falling into the EPT under pollution permits. Our conclusion is that an economy can continue to consider pollution permits as an efficient environmental regulation but proceed with caution given the possibility of being drawn into an EPT.

Open economy macroeconomics of commodity price fluctuation, sectoral inter-linkage and employment

PurposeThis is a theoretical paper in the field of structuralist macroeconomics. The paper focuses on commodity price fluctuation which has emerged as one of the major macroeconomic factors with significant bearing on the relationship between the agricultural and nonagricultural sectors.Design/methodology/approachThe paper develops a dual economy model consisting of an agricultural sector and an industrial sector. The commodity price is subject to the fluctuations due to the fact that stock of primary goods is an asset which is sensitive to speculations. The paper considers a standard methodology of dynamic adjustment process involving change in stock of agricultural goods and price of agricultural goods under perfect foresight. The saddle path properties of the equilibrium are also examined.FindingsThe paper shows that the balanced budget fiscal expansion, capital account liberalization and the agricultural expansion lead to expansion of the industrial sector as well as level of employment. The increase in world interest rate may lead to contraction of the industrial sector and depress employment.Originality/valueWe will consider the openness of the economy in explaining how different macroeconomic policies and capital account liberalization generate multiple cross effects on the inter-connectedness between agricultural and the non-agricultural sector. The paper will discuss the issue of employment generation in conjunction with commodity price fluctuation. We depart from the literature by using Taylor rule under which interest rate is fixed by the Central Bank such that money supply becomes endogenous.

NEW INSIGHTS FROM THE CANONICAL RAMSEY–CASS–KOOPMANS GROWTH MODEL

The present article presents novel results on the Ramsey–Cass–Koopmans growth model. It is shown that the shadow price of capital goes to infinity as the capital stock goes to zero even if all functions are bounded with finite derivatives and that imposing the Inada condition of infinite derivative of the per capita production function at zero stock is irrelevant. It is also shown that unless marginal utility at zero consumption is infinity, there will be a non-empty interval where the Keynes–Ramsey rule does not hold. The paper also shows that the stable saddle path in a phase diagram with the state variable and the shadow price has an unrecognized economic interpretation that enables us to illustrate the value function as the integral of the stable saddle path.

The implications of automation for economic growth when investment decisions are irreversible

This paper discusses automation embedded into a standard growth model without exogenous growth when investment decisions for physical and automation capital are irreversible. The imposed nonnegativity constraints on physical and automation capital induces an imbalance effect between the growth rate of output and the fraction between physical and automation capital. The paper shows that this imbalance effect leads (i) to transitional dynamics off the steady state while (ii) retaining perpetual growth of the AK style in the steady state without exogenous technological progress. We also show that the resulting transition path does not have to be on the saddle path of the system without the nonnegativity constraints.

Policy shocks, current account and the macroeconomy in a developing country

Purpose This is a theoretical paper in the field of international macroeconomics. The purpose of this paper is to focus on a dynamic interaction between current account imbalance and unemployment in response to some policy-induced shocks for a small open economy under a flexible exchange rate. Design/methodology/approach The paper uses a two-sector framework: one sector is traded and another is the non-traded sector that is subject to an effective demand constraint. The current account imbalance arises due to the discrepancy between production of traded goods, household consumption of traded goods and government purchases of importables. The authors keep the asset structure simple by considering only domestic currency and foreign bonds that are imperfect substitutes. The paper considers a standard methodology of dynamic adjustment process involving change in foreign exchange reserves and exchange rate under perfect foresight. The saddle path properties of the equilibrium are also examined. Findings The results of comparative static exercises depend on a set of structural features of a developing country, which include asset substitutability, wage price rigidity and sectoral asymmetries. The paper shows that expansionary monetary policy, balanced budget fiscal expansion and financial liberalization have an ambiguous effect on the current account balance, foreign exchange reserves, non-traded sector and the level of employment. Originality/value The existence of Keynesian unemployment with fixed prices is the key ingredient of this paper. The paper introduces the problem of effective demand to analyze the dynamics of current account balance and exchange rate, which, in turn, determine the sectoral composition of output and level of employment.

Service Good as an Intermediate Input and Optimal Government Policy in an Endogenous Growth Model

The present article considers an endogenous growth model in which the service output is used as intermediate good in commodity sector, tax is imposed on manufacturing product and the revenue earned is invested to create human capital. It is shown that there exists a unique, saddle path stable steady-state growth rate of human capital accumulation and a unique growth-maximizing tax rate. The optimal tax rate for the command economy is compared with growth-maximizing tax rate in competitive economy. A numerical analysis shows that the command economy will have a higher growth rate than the competitive economy. An extension of the model where households privately spend for accumulation of human capital yields the same growth rate as that of the command economy of the previous model. JEL Classification: E6, H2, O4

IS PUBLIC-PRIVATE PARTNERSHIP AN OPTIMAL MODE OF PROVISION OF INFRASTRUCTURE?

The present paper considers a closed economy model with infrastructure service which is an excludable, impure public good, e.g. metro railway service, electricity service, and telephone service etc. The physical capital required by infrastructure sector is provided by public-private partnership. Public and private investment may be complementary or substitute to each other in infrastructure production. We assume government runs a balanced budget. We find there exists unique, saddle path stable growth rate in both the cases. We find that PPP model is optimal in the provision of infrastructure no matter public capital and private capital are a substitute or complementary to each other. But, PPP solution is not growth maximizing in case of substitute relationship between the public capital and private capital. It also makes a comparative study of decentralized economy and command economy. We find that in case of substitute relationship between private capital and public capital, command economy growth rate is higher than the competitive economy growth rate but in the case of complementary relationship between two, command economy growth rate may not be higher than the competitive economy growth rate.

Fossil fuels, alternative energy and economic growth

We present a theoretical framework that incorporates energy within an endogenous growth model. The model explicitly allows for the interaction and substitution between fossil fuels, defined as a non-renewable resource derived from some fixed initial stock, and alternative energy, defined as renewable resource whose production requires capital input. The dynamics of the model depict a unique balance growth to a steady state. The saddle path of consumption temporarily peaks, when fossil fuels are plentiful and cheap, followed by a fall, as fossil fuel become more scarce and alternative energy production has yet to take over, until finally the steady state is reached where alternative energy production fuels the entire economy.The model demonstrates the dynamic substitution of depleting fossil fuel with renewable alternative energy such as to mitigate the negative consequences on growth and welfare of an ever-depleting fuel source in an energy dependent economy. Alternative energy and its potential productivity growth relative to fossil fuels also extends the period of low extraction rates and thereby keeping the finite resource in the ground for longer.The analysis is based on continuous time dynamic simulations that allow for the explicit consideration of transitional dynamics. In particular, the approach highlights the possible short run and medium run non-monotonic paths of consumption, investment and growth, whose analysis are necessarily lost when considering either the steady state equilibrium or deviations from it.

The Rise and Fall of Miracles

It is shown that an economy can grow endogenously in early stage of development. However, the growth is not due to the factors emphasized in the literature but due to abundant labor. If labor is abundant enough to render real wage rate fixed as Lewis (1954) postulated, the marginal product of capital does not decrease with capital and hence endogenous growth emerges. However, the endogenous growth is temporary in the sense that once labor has been fully utilized, the growth enters neoclassical phase in which the economy converges along saddle path to its steady state of low growth. The model is proposed to explain the difference between West German and Japanese growth pattern after World War II. It is argued that West Germany was a highly industrialized Solow (1956) economy far below her steady state due to wartime destruction. As was predicted by Solow, West German growth rate was extremely high initially. However, her growth pace slowed down gradually from the beginning to a low growth steady state. By contrast, Japanese economy after the war was a largely agrarian and labor abundant Lewis economy. Japan's rapid economic growth which had been sustained temporarily for about twenty years before she took the path converging to the present steady state of low growth was endogenous. Almost all of the growth miracles since the latter half of the twentieth century have been of Japanese pattern.

A North-South Model of Economic Growth, Technological Gap, Structural Change and Real Exchange Rate

The aim of this work is to present a model of economic growth, technological gap, structural change and real exchange rate in a formal and theoretical manner, explicitly incorporating the effects of North–South technology gap and the real exchange rate (RER) at a level compatible with its “industrial equilibrium” taking in account the external constraint. In the short term, an increase in the South growth rate of the demand implies that its natural growth rate must also rise, i.e., the level of industry participation and economic productivity should also increase. In the long run the effect of RER on economic growth is conditional on the size of the technological gap and the level of industry participation in South gross domestic product. This condition generates two different dynamics such as a saddle path and multiple equilibriums. To a large extent these results are achieved from the model complex dynamics.

R&D intensity, economic growth and firm-size growth: theory and practice

ABSTRACTThis article proposes a theoretical knowledge-driven horizontal research and development (R&D) endogenous-growth model to explain, for 10 innovative countries, the co-movement of the respective R&D intensity, economic growth and firm-size growth, by exploring short-medium-run and long-run growth effects. Bearing in mind some recent literature, we improve the R&D technology, by considering that R&D is more labour intensive through time as complexity increases, that the diffusion of designs is affected by coordination, organizational and transportation costs, and that a potential entrant will come up with the right idea is reduced because of the presence of a larger number of entrants. We show that when the economy is not initially in a steady state, it can take a saddle path towards the unique and locally saddle-path stable interior steady state. Both transitional-dynamics and steady-state behaviours of our theoretical model are then consistent with, respectively, the time-series and the cross-sectional evidence.