Volume 16, Issue 2 - Recent Advances in Continuous-time Econometrics and Economic Dynamics – Contributions in Honor of Giancarlo Gandolfo

This special issue collects a selection of the papers presented at the conference-Festschrift in honor of Giancarlo Gandolfo held in Rome on September 20-21, 2010. The conference was organized by Giuseppe De Arcangelis (Sapienza University of Rome), Pier Carlo Padoan (OECD and Sapienza University of Rome), Luca Antonio Ricci (International Monetary Fund) and Enrico Saltari (Sapienza University of Rome) with funding by various departments and institutions of Sapienza University of Rome and by the Bank of Italy. The contributions cover many different areas of economic dynamics and continuous-time disequilibrium macroeconomics, two fields to which Giancarlo Gandolfo has been continuously contributing for the last three decades.

We introduce a formula for the optimal savings rate in an economy driven by an investment policy reflecting competitive equilibrium. The reasonable numbers generated by the formula should be of help not only to assess our present situation, but also to prepare our future. Moreover, this paper provides two theorems correcting a widely spread error in economic growth theory, namely that a steady state can be asymptotically reached only if technical progress is labor-augmenting. We finally show that the magnitudes of the optimal savings rates are highly robust to very different, S-shaped evolutions of population and technology. The paper closes with a daring conjecture.

Many monetary and fiscal policy measures have aimed at mitigating the effects of the financial market meltdown that started in the U.S. subprime sector in 2008 and has subsequently spread world wide as a great recession. Slowly some recovery appears to be on the horizon, yet it is worthwhile exploring the fragility and potentially destabilizing feedbacks of advanced macroeconomies in the context of a framework that builds on the ideas of Keynes and Tobin. This framework stresses the fragilities and destabilizing feedback mechanisms that are potential features of all major markets—those for goods, labor, and financial assets. We use a Tobin macroeconomic portfolio approach and the interaction of heterogeneous agents on the financial market to characterize the potential for financial market instability. Though the study of the latter has been undertaken in many partial models, we focus here on the interconnectedness of all three markets. Furthermore, we study what potential labor market, fiscal and monetary policies can have in stabilizing unstable macroeconomies. In order to study this problem we introduce, besides money, long term bonds and equity into the asset market. We in particular propose a countercyclical monetary policy that sells assets in the boom and purchases them in recessions. Modern stability analysis is brought to bear to demonstrate the stabilizing effects of the suggested policies. The policies suggested here could help the Fed in its search for an appropriate exit strategy after its massive intervention in the financial market.

Economic theory does not have a formal model of how announcements of future policies affect economic performance, or how they could be used to manage expectations. In this paper, we show that, in general, the controllability conditions stated by Tinbergen continue to hold under rational expectations. In fact, we find that when they are satisfied, the presence of rational expectations may even enhance our power to control an economy over time through policy announcements. Good communication is therefore crucial. This is important because it shows that an underlying equilibrium can still exist, even if some traditional policy exercises have been special cases that lead to invariance or time inconsistency. Our paper therefore provides a theoretical justification for the recent literature on anchoring expectations so that monetary policy becomes effective enough to achieve or maintain low inflation.

Within a classical discrete-time Cournot oligopoly model with linear demand and quadratic cost functions, minimum and maximum production constraints are imposed in order to explore their effects on the dynamic of the system. Due to the presence of such constraints, the dynamic model assumes the form of a continuous piecewise linear map of the plane. The study of Nash equilibria of the oligopoly game, together with an analytical and numerical investigation of the different kinds of attractors of the dynamical system, shows how the presence of production constraints generates so called border collision bifurcations, a kind of global bifurcations recently introduced in the literature on non-smooth dynamical systems, which gives rise to a quite rich spectrum of dynamic scenarios, characterized by drastic changes in the qualitative dynamic properties of the system.

The last twenty years have seen a marked slowdown of the Italian productivity growth rate. The literature has underlined the role of international factors, such as globalization and adoption of the euro. In this paper we emphasize the role and dynamics of capital accumulation investigating the impact of the introduction of information technology on capital and production in the Italian economy and the extent to which that is being affected by skills in the labour force.The model is specified and estimated as continuous-time general disequilibrium framework. It presents original features: it analyzes the effects of the introduction of the ICT technology on the Italian economy not in a partial equilibrium context of a single market but from a macro point of view where input markets interact; it does not assume that these markets instantaneously clear but rather that there are imperfections and frictions; it does not impose the condition that the economy necessarily converges to a steady state. The model behaves quite well in replicating the dynamics of the Italian economy. It also shows however that there remains some structural inefficiency that worsened in recent years. In fact, our main finding shows that there exists a permanent gap between “optimal” and actual output which increased in the latter part of the sample period. While a fraction of this gap can be attributed to unavoidable (market and non market) adjustment costs some is associated to efficiency losses.

The paper presents a monetary growth model for a small emerging economy with a currency board arrangement. The integration into global financial markets determines an acceleration of debt-creating capital inflows that boosts growth and the prospect of future profits, and leads to the building-up of large imbalances in the public and private sectors. Financial fragility undermines the state of confidence and determines an endogenous capital reversal. At this stage, the strong commitment to maintain the peg leaves no room for stabilization purposes and leads to systemic instability. We run a continuous-time estimation of the non-linear differential equations system of the model, with reference to Argentina during the years of the currency-board arrangement. We find two steady-state solutions, corresponding to a high-interest rate and a low-interest rate equilibrium, respectively. The local stability and sensitivity analysis show that both equilibria are unstable and that the system is intrinsically fragile. We show that even a tighter fiscal policy, according to the prescriptions of international institutions, results ineffective in improving stability.

After an introduction on the mathematical memory formalisms and on their use in many branches of science, we consider a model the evolutions of m > 2 economies yi(t), where we assume that their interaction is based on the differences of the values of their evolution status. Since the economies have bureaucratic structures that cause delays, we introduce in the equations a mathematical memory formalism represented by a derivative of fractional order, which leads to a system of integro-differential equations. The solution of the equations in the Laplace domain is presented as solution of a set of m linear equations in the Laplace Transform (LT) of the yi(t). It is found that the asymptotic values of the state of evolutions of the economies are equal. The case of a system of two economies with different memories is then considered obtaining their evolutions in the time domain expressed as simple monotonically decreasing closed form functions. The asymptotic values of their evolution are also found verifying that they are equal. Numerical and real examples are presented and discussed.

Much of economic theory, especially macro-economics and the study of commodity, financial, and other markets, relies on the use of non-linear structural models to study medium-term and long-run dynamic behaviour of an economy. Continuous-time econometrics is based on the argument that as economic systems are largely continuous they can be better represented and estimated by differential equation rather than difference equation systems. This paper reviews the development of full-information Gaussian estimators of non-linear systems which may then be extended to the estimation of models of intertemporally optimizing agents and other boundary point models, and models where the parameters of the stochastic innovation process enter the deterministic part of the model or vice versa. The long-properties of these models may be studied by calculating the Lyapunov exponents which give information on the form of the attractor the model, the dynamic stability of the model for given parameter values and whether it is structurally stable. The critical dependence of some attractors, and particularly strange attractors, on parameter values emphasizes the need for consistent, efficient estimation. A structural approach provides a rigorous alternative to using single time series to determine whether economic systems exhibit aperiodic or chaotic dynamical behavior.

This paper relates the Central Bank's choice of the target inflation index to expected economic stability in a small open economy that pursues inflation targeting. The analysis is set up in a New Keynesian model that allows for optimal monetary policy in presence of model uncertainty and exogenous shocks. The paper shows that for most of the macrovariables targeting the domestic price index instead of the CPI implies considerably more expected economic stability. When policy makers consider model uncertainty in the design of the optimal policy, the difference in the indexes' performance is sharpened allowing more informed decisions on their convenience.