Studies in Nonlinear Dynamics & Econometrics

Economic Stability and the Choice of the Target Inflation Index

Alessandro Flamini — Thu, 12 Apr 2012 00:19:33 PDT

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.

Continuous-Tme Econometrics of Structural Models

Clifford R. Wymer — Thu, 12 Apr 2012 00:19:31 PDT

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.

The Convergence of Economic Developments

Michele Caputo — Thu, 12 Apr 2012 00:19:30 PDT

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 y_i(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 y_i(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.

The Macrodynamics of External Overborrowing and Systemic Instability in a Small Open Economy

Bernardo Maggi et al. — Thu, 12 Apr 2012 00:19:25 PDT

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.

Technological Adoption with Imperfect Markets in the Italian Economy

Enrico Saltari et al. — Thu, 12 Apr 2012 00:19:22 PDT

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.

Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions

Gian Italo Bischi et al. — Thu, 12 Apr 2012 00:19:20 PDT

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.

Expectations Dynamics: Policy, Announcements and Limits to Dynamic Inconsistency

Andrew Hughes Hallett et al. — Thu, 12 Apr 2012 00:19:18 PDT

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.

Macroeconomic Stabilization Policies in Intrinsically Unstable Macroeconomies

Carl Chiarella et al. — Thu, 12 Apr 2012 00:19:16 PDT

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.

How Much Should a Nation Save? A New Answer

Olivier de La Grandville — Thu, 12 Apr 2012 00:19:09 PDT

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.

The Pricing of Time-Varying Exchange Rate Risk in the Stock Market: A Nonparametric Approach

Y. Peter Chung et al. — Wed, 18 Jan 2012 09:43:49 PST

This paper reexamines the pricing of exchange rate risk in the U.S. stock market. We first construct stock portfolios based on the Foreign Exchange Income (FEI), a measure of currency exposure of firms, reported in their annual reports. We then develop two-factor and multi-factor nonparametric models that allow time variation in risk exposure and risk premium, and nonlinearity in the return generating process. When we assume that risk exposure can be time-varying but risk premium is constant, the estimated premium for exchange rate risk is significant only for the most positive FEI-ranked portfolio and marginally significant for the most negative FEI-ranked portfolio. When we further assume that both risk exposure and risk premium can be time-varying, results suggest that exchange rate risk is significantly priced for all the FEI-ranked portfolios except the one with little exposure.

Flexible Modelling of Duration of Unemployment Using Functional Hazard Models and Penalized Splines: A Case Study Comparing Germany and the UK

Nina Westerheide et al. — Wed, 18 Jan 2012 09:43:46 PST

The intention of this paper is to demonstrate the flexibility and capacity of penalized spline smoothing as estimation routine for modelling duration time data. We investigate the unemployment behaviour in Germany and the UK between 1995 and 2005 based on data from national panel studies. Functional duration time models are used to investigate the dynamics of covariate effects. The focus of our analysis is on contrasting the two economies. The statistical model being employed is built upon the hazard function, where we allow all covariate effects to vary smoothly with time. As result of the analyses, we demonstrate that the most striking difference between the countries is that elderly unemployed in Germany have decreasing chances for reemployment compared to the UK.

Simultaneity and Asymmetry of Returns and Volatilities: The Emerging Baltic States’ Stock Exchanges

Kurt Brännäs et al. — Wed, 18 Jan 2012 09:43:42 PST

The paper suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks and exogenous variables. The model is employed to study the three closely related Baltic States’ stock exchanges and the influence exerted by the Russian stock exchange. Using daily data, we find recursive structures with returns in Riga directly depending on returns in Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities, both Riga and Vilnius depend on Tallinn. In addition, we find evidence of asymmetric effects of shocks arising in Moscow and in Baltic States on both returns and volatilities.

Asymmetric Unemployment Rate Dynamics in Australia

Gunnar Bårdsen et al. — Wed, 18 Jan 2012 09:43:38 PST

The unemployment rate in Australia is modelled as an asymmetric and nonlinear function of aggregate demand, productivity, real interest rates, the replacement ratio and the real exchange rate. If changes in unemployment are big, the management of of demand, real interest rates and the replacement ratio will be good instruments to start bringing it down. The model is developed by exploiting recent developments in automated model-selection procedures.

Forecasting U.S. Output Growth with Non-Linear Models in the Presence of Data Uncertainty

Michael P. Clements — Wed, 18 Jan 2012 09:43:35 PST

We consider the impact of data revisions on the forecast performance of a SETAR regime-switching model of U.S. output growth. The impact of data uncertainty in real-time forecasting will affect a model's forecast performance via the effect on the model parameter estimates as well as via the forecast being conditioned on data measured with error. We find that benchmark revisions do affect the performance of the non-linear model of the growth rate, and that the performance relative to a linear comparator deteriorates in real-time compared to a pseudo out-of-sample forecasting exercise.

Band-Limited Stochastic Processes in Discrete and Continuous Time

D.S.G. Pollock — Wed, 18 Jan 2012 09:43:31 PST

A theory of band-limited linear stochastic processes is described and it is related to the familiar theory of ARMA models in discrete time. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by re-sampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process.

Stages of Economic Development in an Innovation-Education Growth Model

Manuel A. Gómez — Mon, 19 Sep 2011 14:33:05 PDT

Physical capital accumulation, knowledge formation and R&D-based technological progress are considered the three main sources of growth. The common view is that they characterize, in a temporal order, the three phases that a typical advanced economy passes through in its development process. Recently it has been argued, however, that an innovation-education sequence could agree better than an education-innovation transition with the empirical fact that the rise in formal education to the masses follows rather than precedes the process of industrialization. Accordingly, this paper devises an endogenous growth model with physical capital, human capital and R&D that, unlike previous related work, is able to generate adjustment dynamics in which the innovative stage precedes knowledge formation, consistent with empirical evidence.

Constrained k-class Estimators in the Presence of Weak Instruments

Emma M. Iglesias — Mon, 19 Sep 2011 14:33:03 PDT

In this paper, we show how we can apply the existing theory when a parameter is on a boundary (see Andrews (1999, 2000) and Iglesias and Linton (2007)) in the context of weak instruments. When we have a priori knowledge of the signs of the relationships between the instruments and the endogenous variables, we can construct constrained k-class estimators (a special case is a constrained 2SLS estimator), where the asymptotic theory in the presence of weak instruments changes in relation to the traditional weak-instrument asymptotics of the unconstrained k-class estimators of Staiger and Stock (1997). We show theoretically and in a simulation study the advantages that we have by constraining the estimator.

Panel Cointegration Rank Testing with Cross-Section Dependence

Josep Lluis Carrion-i-Silvestre et al. — Mon, 19 Sep 2011 14:33:00 PDT

In this paper, we propose a test statistic to determine the cointegration rank of VAR processes in panel data allowing for cross-section dependence among the time series in the panel data. The cross-section dependence is accounted for through the specification of an approximate common factor model, which covers situations where there is cointegration among the cross-section dimension. Finite sample performance is investigated via a Monte Carlo experiment. We show that in some cases not accounting for common factors when they are present can lead to overestimating the cointegrating rank. We apply our proposed tests to two empirical applications and find strong evidence for panel cointegration once common factors are accounted for.

A Computationally Practical Robust Simulation Estimator for Dynamic Panel Tobit Models

Sheng-Kai Chang — Mon, 19 Sep 2011 14:32:58 PDT

In this paper, a computationally robust simulation estimator is proposed for the dynamic panel Tobit model with large categories of dependence structures. The maximum simulated likelihood estimators are obtained through a recursive algorithm formulated by Geweke-Hajivassiliou-Keane and Gibbs sampling simulators. Monte Carlo experiments indicate that the proposed robust simulation estimators perform well under the errors having a heavy-tailed distribution, even for a small simulation size. The initial conditions problem is also investigated for the robust simulation estimators through Monte Carlo experiments.

Beta Autoregressive Transition Markov-Switching Models for Business Cycle Analysis

Monica Billio et al. — Mon, 19 Sep 2011 14:32:55 PDT

We propose a new class of Markov-switching models useful for business cycle analysis, with transition probabilities following independent beta autoregressive processes. We study the effects of the autoregressive dynamics on the regime duration. We propose a full Bayesian inference approach and particular attention is paid to the parameters of the latent beta autoregressive processes. We discuss the choice of the prior distributions and propose a Markov-chain Monte Carlo algorithm for estimating both the parameters and the latent variables. Finally, we provide an application to the Euro area business cycle.