Global Indeterminacy Research Articles

The perils of fiscal feedback rules

This paper introduces a fiscal feedback rule (FFR) in an endogenous growth model with public debt dynamics. We assume that part of the debt burden is covered by tax increases (we name this “sterilization”), while the remaining part is financed by issuing new debt. We show that while low sterilization does not ensure the existence of a long-run steady state, high sterilization can lead to multiple steady states and aggregate instability in the form of local and global indeterminacy, potentially condemning the economy to a low-growth/high-debt trap steady state and long-lasting public debt cycles. By combining econometric estimations and a calibration exercise on developed economies, we highlight that these various perils can occur for empirically plausible values of the sterilization coefficient.

Imperfect competition in the banking sector and economic instability

We study the impact of competition in the banking sector on the emergence of endogenous cycles driven by self-fulling volatile expectations. We consider an OLG model with two sectors and two household types: workers, who consume and work when young and save through bank deposits; and entrepreneurs, who seek bank loans to finance current consumption and to invest in a productive technology that transforms the consumption good into capital. When old, entrepreneurs rent this capital to firms, who produce the consumption good using capital and labor. All markets are perfectly competitive, except the loans market where banks compete à la Cournot under free entry and exit.In the absence of externalities in the capital producing technology, more competition in the banking sector promotes the emergence of local indeterminacy and sunspots fluctuations. In contrast, under constant social returns to scale in the capital producing technology, bank market power alone triggers the emergence of local indeterminacy. With increasing social returns to scale, both market power and externalities facilitate the emergence of local indeterminacy. Additionally, when banks have market power, steady state multiplicity may emerge, opening the way to global indeterminacy and fluctuations.

Making Law Possible

Making Law Possible

Fiscal Stimulus of Last Resort

AbstractI examine global dynamics in a monetary model with overlapping generations of finite‐horizon agents, nonseparable preferences over consumption and real money balances, and a binding lower bound on nominal interest rates. Debt targeting rules exacerbate the possibility of self‐fulfilling liquidity traps, for agents expect austerity following deflationary slumps. Conversely, activist but sustainable fiscal policy regimes—implementing intertemporally balanced tax cuts and/or transfer increases in response to disinflationary trajectories—are capable of escaping liquidity traps and embarking inflation into a globally stable path that converges to the target. Should fiscal stimulus of last resort be overly aggressive, however, spiral dynamics around the liquidity‐trap steady state exist, causing global indeterminacy.

Local and global indeterminacy and transition dynamics in a growth model with public goods

Local and global indeterminacy and transition dynamics in a growth model with public goods

Sovereign debt, fiscal policy, and macroeconomic instability

We study the relation between capital accumulation, fiscal policy, and sovereign debt dynamics in a small open economy. The government maximizes spending, facing borrowing constraints and a conditionality requirement. Debt dynamics are forward looking, being driven by the endogenous borrowing constraint. Current debt is determined by expectations about the government's ability to finance itself in the future, opening the room for indeterminacy. If the government believes it may issue more debt next period, the borrowing constraint relaxes, and current debt increases. The government invests more in productive activities, generating a boom which increases tax revenues. However, as this increase does not repay the additional debt, the government will issue more debt next period, confirming initial expectations. To exclude explosive trajectories, tax revenues must increase enough to repay the outstanding debt and reduce future debt emission. This is possible only with a sufficiently procyclical tax rate. In this case, if productive externalities are large enough, the economy exhibits local and global indeterminacy, as steady-state multiplicity is also obtained. Avoiding sufficiently procyclical tax rates, the government can prevent local and global fluctuations driven by self-fulfilling volatile expectations. This differs from the general wisdom that procyclical tax rates should be used for stabilization.

Maladaptation to environmental degradation and the interplay between negative and positive externalities

This paper investigates the possible dynamics that may emerge in an economy in which agents adapt to environmental degradation by increasing the produced output to repair the damages of environmental degradation. The analyzed economy is characterized by both positive and negative externalities. On the one hand, an increase in production-related environmental degradation lowers the net income left at disposal for consumption and investment; on the other hand, it induces an increase in labor and capital to repair environmental damages from production, which enhances the positive externalities occurring in the production process. From the analysis of the model we show that there can be two steady states but only the one with lower capital level can be locally attractive. Both local and global indeterminacy may arise in the model, even with decreasing returns to scale. It follows that one cannot predict a priori which path the economy will follow when converging to an equilibrium, nor the equilibrium the dynamics will eventually converge to. In particular, the trajectories emerging from the model may eventually lead the economy to be trapped in a Pareto-dominated equilibrium with lower capital and higher environmental degradation levels. Moreover, the interplay between positive and negative externalities generates a rich set of possible trajectories that may lead to opposite extreme outcomes, namely, either infinite growth or the collapse of the economy.

Shilnikov chaos, low interest rates, and New Keynesian macroeconomics

The paper shows that in a New Keynesian (NK) model, an active interest rate feedback monetary policy, when combined with a Ricardian passive fiscal policy, à la Leeper-Woodford, may induce the onset of a Shilnikov chaotic attractor in the region of the parameter space where uniqueness of the equilibrium prevails locally. Implications, ranging from long-term unpredictability to global indeterminacy, are discussed in the paper. We find that throughout the attractor, the economy lingers in particular regions, within which the emerging aperiodic dynamics tend to evolve for a long time around lower-than-targeted inflation and nominal interest rates. This can be interpreted as a liquidity trap phenomenon, produced by the existence of a chaotic attractor, and not by the influence of an unintended steady state or the Central Bank's intentional choice of a steady state nominal interest rate at its lower bound. In addition, our finding of Shilnikov chaos can provide an alternative explanation for the controversial “loanable funds” over-saving theory, which seeks to explain why interest rates and, to a lesser extent, inflation rates have declined to current low levels, such that the real rate of interest may be below the marginal product of capital. Paradoxically, an active interest rate feedback policy can cause nominal interest rates, inflation rates, and real interest rates unintentionally to drift downwards within a Shilnikov attractor set. Our results are robust to whether money is in the production function, in the utility function, or not in the model at all. But our results do depend upon the existence of sticky prices.

Growth and instability in a small open economy with debt

The relationship between public debt, growth and volatility is investigated in a Barro-type (1990) endogenous growth model, with three main features: we consider a small open economy, international borrowing is constrained and households have taste for domestic public debt. Therefore, capital, public debt and the international asset are not perfect substitutes and the economy is characterized by an investment multiplier. Whatever the level of the debt-output ratio, the existing BGP features expectation-driven fluctuations. If the debt-output ratio is low enough, there is also a second BGP with a lower growth rate. Hence, a lower debt does not stabilize the economy with credit market imperfections. However, a high enough taste for domestic public debt may rule out the BGP with lower growth. This means that if the share of public debt held by domestic households is high enough, global indeterminacy does not occur.

Environmental degradation and indeterminacy of equilibrium selection

<p style='text-indent:20px;'>This paper analyzes an intertemporal optimization problem in which agents derive utility from three goods: leisure, a public environmental good and the consumption of a produced good. The global analysis of the dynamic system generated by the optimization problem shows that global indeterminacy may arise: given the initial values of the state variables, the economy may converge to different steady states, by choosing different initial values of the control variable.</p>

The failure of stabilization policy: Balanced-budget fiscal rules in the presence of incompressible public expenditures

We consider an infinite horizon neoclassical model with a government that (i) balances its budget at each point in time, (ii) faces unavoidable (incompressible) public expenditures, and (iii) further uses a fiscal rule for the share of variable government spending in output with the purpose of stabilizing the economy. We show that insulating this economy from belief driven fluctuations is not possible if the government finances these two components of public spending using a distortionary proportional income tax. In this case, we always have steady state multiplicity (two steady states) and global indeterminacy, while local indeterminacy is also possible. More precisely, even if a sufficiently procyclical share of the variable government spending component in output is still able to eliminate local indeterminacy, two saddle steady states prevail, so that, depending on expectations, the economy may either converge to the low steady state or to the high steady state. This implies that a regime switching rational expectation equilibrium, where the economy switches between paths converging to the two different steady states, easily arises. As expectations influence long run outcomes, our model is able to generate large and sudden expansions and contractions in response to expectation shocks.

Chaos control in presence of financial bubbles

The paper shows that in the economy described by Miao and Wang (2015), with financial bubbles emerging in the banking sector, a Shilnikov chaotic attractor giving rise to unpredictable global indeterminacy can appear when the bubble bursts, resulting in a financial crisis. In this case, a suitable policy algorithm to eliminate or control the chaotic dynamics is proposed.

Art Forms Emerging: An Approach to Evaluative Diversity in Art

ABSTRACTArtworks are rationally evaluable and comparable within their art form, but not from outside. Beethoven's string quartets cannot be evaluated against works of Hindustani music. This is the problem of evaluative diversity: local commensurability, global indeterminacy. This article sketches an approach to the problem based on novel conceptions of aesthetic pleasure and cultural learning, and on the Darwinian Principle of Divergence as applied to cultural evolution.

Living in an uncertain world: Environment substitution, local and global indeterminacy

Environmental problems are increasingly frequent, intensive and unpredictable. To protect from the observed environmental depletion, economic agents increasingly react by substituting previously free public environmental goods with costly private goods. This substitution mechanism, however, can contribute to enhance the indeterminacy of the possible consequences of mankind activity, further increasing the uncertainty on the future environmental trajectories. To investigate this issue, the paper proposes an intertemporal optimization problem in which agents derive utility from three goods: leisure, a public environmental good and/or private consumption that can be used as a substitute for the environment. The analysis shows that the economy may end up being trapped in the Pareto-dominated steady state and that both local and global indeterminacy may arise in the model. No indeterminacy, however, emerges if green technologies are used so that production has no negative effects on the environment.

Mathematical analysis of an economic growth model with perfect-substitution technologies

The purpose of this paper is to highlight certain features of a dynamic optimisation problem in an economic growth model with environmental negative externalities that gives rise to a two-dimensional dynamical system. In particular, it is demonstrated that the dynamics of the model, which is based on a production function with perfect substitutability (perfect substitution technologies), admits a locally attracting equilibrium with a basin of attraction that may be considerably large, as it can extend up to the boundary of the system phase plane. Moreover, this model exhibits global indeterminacy because either equilibrium of the system can be selected according to agent expectation. Formulas for the calculation of the bifurcation coefficients of the system are derived, and a result on the existence of limit cycles is obtained. A numerical example is given to illustrate the results.

Indeterminate equilibrium growth with product and R&D spillovers

The paper revisits an endogenously growing economy à la Romer (1990) to explore the possibility of local and global indeterminacy where, along with the usual R&D spillover, a manufacturing sector generates a product spillover on R&D. When the product spillover facilitates R&D, the dynamic market equilibrium is unique and determinate. However, when the product spillover is strongly negative on R&D, multiple balanced market equilibria emerge and are therefore globally indeterminate. Furthermore, global indeterminacy coexists with local indeterminacy under the joint condition on the intertemporal elasticity of substitution of consumption. Local indeterminacy also emerges when the product spillover is mildly negative in tandem with a high intertemporal elasticity of substitution. Hence, a dynamic market economy with product spillovers in the R&D sector enriches the understanding of observable growth phenomena, including business and growth cycles and income and growth disparity, among countries with the same economic fundamentals.

GLOBALLY INDETERMINATE GROWTH PATHS IN THE LUCAS MODEL OF ENDOGENOUS GROWTH

This paper shows that global indeterminacy may characterize the three-dimensional vector field implied by the Lucas [(1988)Journal of Monetary Economics22, 3–42] endogenous growth model. To achieve this result, we demonstrate the emergence of a family of homoclinic orbits connecting the steady state to itself in backward and forward time, when the stable and unstable manifolds are locally governed by real eigenvalues. In this situation, we prove that if the saddle quantity is negative, and other genericity conditions are fulfilled, a stable limit cycle bifurcates from the homoclinic orbit. Orbits originating in a tubular neighborhood of the homoclinic orbit are then bound to converge to this limit cycle, creating the conditions for the onset of global indeterminacy. Some economic intuitions related to this phenomenon are finally explored.

Time‐varying consumption tax, productive government spending, and aggregate instability

AbstractIn this paper we investigate if government balanced‐budget rules together with endogenous taxation may lead to aggregate instability in an endogenous growth framework. After highlighting the differences with the exogenous growth framework, we prove that under counter‐cyclical consumption taxes, while there exists a unique balanced growth path, sunspot equilibria based on self‐fulfilling expectations occur through a form of global indeterminacy. In addition, we argue that this result is empirically plausible for a large set of OECD countries and that it may also emerge with endogenous income taxes.

Trade and indeterminacy revisited

AbstractWe consider a dynamic two‐country model of trade with production externalities with an emphasis on the possibility of global indeterminacy, which means that the distribution of capital stocks in each country in the long run depends on households’ expectations. Opening trade yields expectation‐driven fluctuations. Global indeterminacy may occur around the free trade steady states even when the autarkic steady states are saddle points in both countries, and it must happen when local indeterminacy occurs around the autarkic steady states in both countries.

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.