Observability and Structural Identifiability of Nonlinear Biological Systems

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations, and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods for Identification and Modelling of Complex Biological Systems" of Complexit

Regional convergence, polarization and mobility in the European Union, 1980-1996

The aim of the paper is to analyse how the regional convergence, polarization and mobility have evolved in the EU from 1980 onwards. Using both simple and weighted indicators, the paper not only shows that all these three processes have been going on but that there are no sings of polarization and that the mobility degree (taken into account the whole period) is quite high. At the same time, the paper shows that the rate of convergence and the degree of mobility have declined, rising doubts about what may happen in the near future.

The Econometrics of DSGE Models

In this paper, I review the literature on the formulation and estimation of dynamic stochastic general equilibrium (DSGE) models with a special emphasis on Bayesian methods. First, I discuss the evolution of DSGE models over the last couple of decades. Second, I explain why the profession has decided to estimate these models using Bayesian methods. Third, I briefly introduce some of the techniques required to compute and estimate these models. Fourth, I illustrate the techniques under consideration by estimating a benchmark DSGE model with real and nominal rigidities. I conclude by offering some pointers for future research.DSGE Models, Likelihood Estimation, Bayesian Methods

Migratory flows in Spain: a nonparametric and semiparametric approach

Labour market is characterized in Spain by a high persistence in unemployment rates. One of the main reasons of this persistence is the lack of labour mobility. The present paper addresses this issue empirically and analyses the determinants of migration in Spain from a regional standpoint. We used a panel data set that includes annual bilateral migratory flows between the 17 Spanish regions from 1995 through 2000. For this purpose, after a descriptive analysis, we develop a nonparametric approach to show the factors that influence in the magnitude of migratory flows. Later on, semiparametric estimation techniques are applied to provide more econometric evidence regarding migratory flows. Main conclusions are as follows: first, a high inertia in the migratory flows exists, that it is to say, migratory movements are very persistent; second, migratory flows mainly respond, though weakly, to the differentials of wages, unemployment rates and house prices between regions; third, migratory flows are also affected, to a great extent, by non economic factors. Keywords: migratory flows, regions, unemployment, wages. JEL classification: J61, R23, C14

Okun's law in the Spanish regions

The purpose of this paper is to analyse Okun's law for Spain and its seventeen regions over the period 1980-2004. Based on its “gap†specification and using two different detrending techniques, the results show that an inverse relationship between unemployment and output holds for most of the Spanish regions and for the whole country. However, the quantitative values of Okun''s coefficients for these regions are quite different. In addition, the coefficients for each region varied across the two detrending techniques. Even so, these coefficients are lower than those initially estimated by Okun and others.

Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data

This paper uses a seminonparametric model and Consumer Expenditure Survey data to estimate life cycle profiles of consumption, controlling for demographics, cohort and time e.ects. In addition to documenting profiles for total and nondurable consumption, we devote special attention to the age expenditure pattern for consumer durables. We find hump-shaped paths over the life cycle for total, for nondurable and for durable expenditures. Changes in household size account for roughly half of these humps. The other half remains unaccounted for by the standard complete markets life cycle model. Our results imply that households do not smooth consumption over their lifetimes. This is especially true for services from consumer durables. Bootstrap simulations suggest that our empirical estimates are tight and sensitivity analysis indicates that the computed profiles are robust to a large number of different specifications.