A low dimensional Kalman filter for systems with lagged observables

This note describes how the Kalman filter can be modified to allow for thevector of observables to be a function of lagged variables without increasing the dimensionof the state vector in the filter. This is useful in applications where it is desirable to keepthe dimension of the state vector low. The modified filter and accompanying code (whichnests the standard filter) can be used to compute (i) the steady state Kalman filter (ii) thelog likelihood of a parameterized state space model conditional on a history of observables(iii) a smoothed estimate of latent state variables and (iv) a draw from the distribution oflatent states conditional on a history of observables.

Externalities and interdependent growth: Theory and evidence

I formulate and estimate a model of externalities within countriesand technological interdependence across countries. I find that externalreturns to scale to physical capital within countries are 8 percent; thata 10 percent increase of total factor productivity of a country's neighborsraises its total factor productivity by 6 percent; and that a 2 percentannual growth rate of labor productivity can be explained as an endogenousresponse to an exogenous 0.2 percent annual growth rate of total factorproductivity in the steady--state.

North-South convergence and the allocation of CO2 emissions

We postulate a two-region world, comprised of North (calibrated after the US) and South(calibrated after China). Our optimization results show the compatibility of the following threedesiderata:(1) Global CO2 emissions follow a conservative path that leads to the stabilizationof concentrations at 450 ppm.(2) North and South converge to a path of sustained growth at 1% per year (28.2%per generation) in 2075.(3) During the transition to the steady state, North also grows at 1% per year whileSouth s rates of growth are markedly higher.The transition paths require a drastic reduction of the share of emissions allocated to North,large investments in knowledge, both in North and South, as well as very large investments ineducation in South. Surprisingly, in order to sustain North s utility growth rate, some output mustbe transferred from South to North during the transition.Although undoubtedly subject to many caveats, our results support a degree of optimism byproviding prima facie evidence of the possibility of tackling climate change in a way that is fairboth across generations and across regions while allowing for positive rates of humandevelopment.

Stable sunspot equilibria in a cash-in-advance economy

We analyze a monetary model with flexible labor supply, cash-inadvance constraints and seigniorage-financed government deficits. If the intertemporal elasticity of substitution of labor is greater than one, there are two steady states, one determinate and the other indeterminate. If the elasticity is less than one, there is a unique steady state, which can be indeterminate. Only in the latter case do there exist sunspot equilibria that are stable under adaptive learning. A sufficient reduction in government purchases can in many cases eliminate the sunspot equilibria while raising consumption/labor taxes even enough to balance the budget may fail to achieve determinacy.

Malthusian dynamism and the rise of Europe: Make war, not love

This paper argues that Malthusian regimes are capable of sustained changes in per capita incomes. Shifting mortality and fertility schedules can lead to different steady-state income levels, with long periods of growth during the transition. Europe checked the downward pressure on wages through late marriage, which reduced fertility, and a mortality regime that combined high death rates with high incomes. We argue that both emerged as a result of the Black Death.

Markups, gaps and the welfare costs of business fluctuations

In this paper we present a simple theory-based measure of the variations in aggregate economic efficiency: the gap between the marginal product of labor and the household s consumption/leisure tradeoff. We show that this indicator corresponds to the inverse of the markup of price over social marginal cost, and give some evidence in support of this interpretation. We then show that, with some auxilliary assumptions our gap variable may be used to measure the efficiency costs of business fluctuations. We find that the latter costs are modest on average. However, to the extent the flexible price equilibrium is distorted,the gross efficiency losses from recessions and gains from booms may be large. Indeed, we find that the major recessions involved large efficiency losses. These results hold for reasonable parameterizations of the Frisch elasticity of labor supply, the coefficient of relative risk aversion, and steady state distortions.

The three horsemen of riches: Plague, war and urbanization in early modern Europe

How did Europe escape the "Iron Law of Wages?" We construct a simple Malthusian model withtwo sectors and multiple steady states, and use it to explain why European per capita incomes andurbanization rates increased during the period 1350-1700. Productivity growth can only explain a smallfraction of the rise in output per capita. Population dynamics changes of the birth and death schedules were far more important determinants of steady states. We show how a major shock to population cantrigger a transition to a new steady state with higher per-capita income. The Black Death was such ashock, raising wages substantially. Because of Engel's Law, demand for urban products increased, andurban centers grew in size. European cities were unhealthy, and rising urbanization pushed up aggregatedeath rates. This effect was reinforced by diseases spread through war, financed by higher tax revenues.In addition, rising trade also spread diseases. In this way higher wages themselves reduced populationpressure. We show in a calibration exercise that our model can account for the sustained rise in Europeanurbanization as well as permanently higher per capita incomes in 1700, without technological change.Wars contributed importantly to the "Rise of Europe", even if they had negative short-run effects. We thustrace Europe s precocious rise to economic riches to interactions of the plague shock with the belligerentpolitical environment and the nature of cities.

A positive theory of geographic mobility and social insurance

This paper presents a tractable dynamic general equilibrium model thatcan explain cross-country empirical regularities in geographical mobility,unemployment and labor market institutions. Rational agents vote overunemployment insurance (UI), taking the dynamic distortionary effects ofinsurance on the performance of the labor market into consideration.Agents with higher cost of moving, i.e., more attached to their currentlocation, prefer more generous UI. The key assumption is that an agent'sattachment to a location increases the longer she has resided there. UIreduces the incentive for labor mobility and increases, therefore, thefraction of attached agents and the political support for UI. The mainresult is that this self-reinforcing mechanism can give rise to multiplesteady-states-one 'European' steady-state featuring high unemployment,low geographical mobility and high unemployment insurance, and one'American' steady-state featuring low unemployment, high mobility andlow unemployment insurance.

Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

Bistability of mitochondrial respiration underlies paradoxical reactive oxygen species generation induced by anoxia

Increased production of reactive oxygen species (ROS) in mitochondria underlies major systemic diseases, and this clinical problem stimulates a great scientific interest in the mechanism of ROS generation. However, the mechanism of hypoxia-induced change in ROS production is not fully understood. To mathematically analyze this mechanism in details, taking into consideration all the possible redox states formed in the process of electron transport, even for respiratory complex III, a system of hundreds of differential equations must be constructed. Aimed to facilitate such tasks, we developed a new methodology of modeling, which resides in the automated construction of large sets of differential equations. The detailed modeling of electron transport in mitochondria allowed for the identification of two steady state modes of operation (bistability) of respiratory complex III at the same microenvironmental conditions. Various perturbations could induce the transition of respiratory chain from one steady state to another. While normally complex III is in a low ROS producing mode, temporal anoxia could switch it to a high ROS producing state, which persists after the return to normal oxygen supply. This prediction, which we qualitatively validated experimentally, explains the mechanism of anoxia-induced cell damage. Recognition of bistability of complex III operation may enable novel therapeutic strategies for oxidative stress and our method of modeling could be widely used in systems biology studies.

X-ray photoelectron spectroscopy analysis of ion¿beam¿induced oxidation of GaAs and AlGaAs

The oxidation of GaAs and AlGaAs targets subjected to O2+ bombardment has been analyzed, using in situ x¿ray photoelectron spectroscopy, as a function of time until steady state is reached. The oxides formed by the O2+ bombardment have been characterized in terms of composition and binding energy. A strong energy and angular dependence for the oxidation of As relative to Ga is found. Low energies as well as near normal angles of incidence favor the oxidation of As. The difference between Ga and As can be explained in terms of the formation enthalpy for the oxide and the excess supply of oxygen. In an AlGaAs target the Al is very quickly completely oxidized irrespective of the experimental conditions. The steady state composition of the altered layers show in all cases a preferential removal of As.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Defect dynamics in viscous fingering

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.