Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

The peroxiredoxin Tpx1 is essential as a H202-scavenger during aerobic growth in fission yeast

Peroxiredoxins are known to interact with hydrogen peroxide (H2O2) and to participate in oxidant scavenging, redox signal transduction, and heat-shock responses. The two-cysteine peroxiredoxin Tpx1 of Schizosaccharomyces pombe has been characterized as the H2O2 sensor that transduces the redox signal to the transcription factor Pap1. Here, we show that Tpx1 is essential for aerobic, but not anaerobic, growth. We demonstrate that Tpx1 has an exquisite sensitivity for its substrate, which explains its participation in maintaining low steady-state levels of H2O2. We also show in vitro and in vivo that inactivation of Tpx1 by oxidation of its catalytic cysteine to a sulfinic acid is always preceded by a sulfinic acid form in a covalently linked dimer, which may be important for understanding the kinetics of Tpx1 inactivation. Furthermore, we provide evidence that a strain expressing Tpx1.C169S, lacking the resolving cysteine, can sustain aerobic growth, and we show that small reductants can modulate the activity of the mutant protein in vitro, probably by supplying a thiol group to substitute for cysteine 169.

Poverty and children's work in Spain and Latin America. Some preliminary remarks.

In the first part of this paper we try to test the relationship between mothers earnings, fertility and children's work in the Spanish (Catalan) context of the first third of the 20th century. Specific human capital investment of adult working women had as an outcome the sharp increase of their real wage and also the increase of the opportunity cost of time devoted to house work including child rearing. Fertility evolution is endogenous to the model and decreases as a result of women real wage increases. Human capital investment of labouring women and mandatory schooling of children shift the labour supply function to a new steady state in which the slope is steeper. According to recent papers this model applies to 20th century Spain and it causes the abolition of children's work. Nonetheless the model do not apply to 20th century Latin America. Despite the positive evolution of literacy and life expectancy in this region, other factors involved poor results of the educational human capital investment. In this paper we remark the role of the increasing share of the informal sector of the economy ruled on the bases of women's and children's work. Second we stress the role of high income inequality evolution and endogamic school supplies to explain the limits of increasing literacy on more remarkable human capital improvements.

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 role of moral values in the economic analysis of crime: A general equilibrium approach

In this paper, we develop a general equilibrium model of crime and show thatlaw enforcement has different roles depending on the equilibrium characterization and the value of social norms. When an economy has a unique stable equilibrium where a fraction of the population is productive and the remaining predates, the government can choose an optimal law enforcement policy to maximize a welfare function evaluated at the steady state. If such steady state is not unique, law enforcement is still relevant but in a completely different way because the steady state that prevails depends on the initial proportions of productive and predator individuals in the economy. The relative importance of these proportions can be changed through law enforcement policy.

Adaptive learning in models with lagged variables

In this work I study the stability of the dynamics generated by adaptivelearning processes in intertemporal economies with lagged variables. Iprove that determinacy of the steady state is a necessary condition for the convergence of the learning dynamics and I show that the reciprocal is not true characterizing the economies where convergence holds. In the case of existence of cycles I show that there is not, in general, a relationship between determinacy and convergence of the learning process to the cycle. I also analyze the expectational stability of these equilibria.

Testing for convergence clubs in income per-capita: A predictive density approach

The paper proposes a technique to jointly test for groupings of unknown size in the cross sectional dimension of a panel and estimates the parameters of each group, and applies it to identifying convergence clubs in income per-capita. The approach uses the predictive density of the data, conditional on the parameters of the model. The steady state distribution of European regional data clusters around four poles of attraction with different economic features. The distribution of incomeper-capita of OECD countries has two poles of attraction and each grouphas clearly identifiable economic characteristics.

Hybrid consumption paths in the attribute space: A model and application with scanner data

This paper presents and estimates a dynamic choice model in the attribute space considering rational consumers. In light of the evidence of several state-dependence patterns, the standard attribute-based model is extended by considering a general utility function where pure inertia and pure variety-seeking behaviors can be explained in the model as particular linear cases. The dynamics of the model are fully characterized by standard dynamic programming techniques. The model presents a stationary consumption pattern that can be inertial, where the consumer only buys one product, or a variety-seeking one, where the consumer shifts among varied products.We run some simulations to analyze the consumption paths out of the steady state. Underthe hybrid utility assumption, the consumer behaves inertially among the unfamiliar brandsfor several periods, eventually switching to a variety-seeking behavior when the stationary levels are approached. An empirical analysis is run using scanner databases for three different product categories: fabric softener, saltine cracker, and catsup. Non-linear specifications provide the best fit of the data, as hybrid functional forms are found in all the product categories for most attributes and segments. These results reveal the statistical superiority of the non-linear structure and confirm the gradual trend to seek variety as the level of familiarity with the purchased items increases.

Corruption and the Hadleyburg effect

We study the dynamics of corruption relying on two fundamental observations:(a) Given agents detected as corrupt are typically fired and replaced, the historical levels of corruption have an impact on current corruption throughthe distribution of corruption costs of old agents; (b) Institutions negatively affected by their agents' corrupt activities are likely to respond optimally to it thereby decreasing the payoff from being corrupt. We model this situation by considering an agent who is supposed to monitor acontractor's delivery of a product or service and can manipulate hisreports thus allowing the contractor to deliver lower quality in exchange for a bribe. Given the two generations of agents overlapping at any particular date, the administration sets an optimal level of quality in eachperiod. We find that (i) A unique steady state level of corruption exists;(ii) Regardless of the initial distribution, apart from an initial period,equilibrium sequences are decreasing and converge to the steady state, aresult we term the "Hadleyburg effect". We use these findings to study thedynamic response of corruption to both temporary and permanent shocks to theprofitability of corruption and we find that the "Hadleyburg effect" hasimportant positive and normative implications.

Banks, liquidity crises and economic growth

How do the liquidity functions of banks affect investment and growth at different stages ofeconomic development? How do financial fragility and the costs of banking crises evolve with the level of wealth of countries? We analyze these issues using an overlapping generations growth model where agents, who experience idiosyncratic liquidity shocks, can invest in a liquid storage technology or in a partially illiquid Cobb Douglas technology. By pooling liquidity risk, banks play a growth enhancing role in reducing inefficient liquidation of long term projects, but they may face liquidity crises associated with severe output losses. We show that middle income economies may find optimal to be exposed to liquidity crises, while poor and rich economies have more incentives to develop a fully covered banking system. Therefore, middle income economies could experience banking crises in the process of their development and, as they get richer, they eventually converge to a financially safe long run steady state. Finally, the model replicates the empirical fact of higher costs of banking crises for middle income economies.

Equilibrium unemployment insurance

In this paper, we incorporate a positive theory of unemployment insuranceinto a dynamic overlapping generations model with search-matching frictionsand on-the-job learning-by-doing. The model shows that societies populatedby identical rational agents, but differing in the initial distributionof human capital across agents, may choose very different unemploymentinsurance levels in a politico-economic equilibrium. The interactionbetween the political decision about the level of the unemployment insuranceand the optimal search behavior of the unemployed gives rise to aself-reinforcing mechanism whichmay generate multiple steady-stateequilibria. In particular, a European-type steady-state with highunemployment, low employment turnover and high insurance can co-exist withan American-type steady-state with low unemployment, high employment turnoverand low unemployment insurance. A calibrated version of the model featurestwo distinct steady-state equilibria with unemployment levels and durationrates resembling those of the U.S. and Europe, respectively.

The poor stay poor: Non-convergence across countries and regions

We study the issue of income convergence across countries and regions witha Bayesian estimator which allows us to use information in an efficient andflexible way. We argue that the very slow convergence rates to a commonlevel of per-capita income found, e.g., by Barro and Xavier Sala-i-Martin,is due to a 'fixed effect bias' that their cross-sectional analysisintroduces in the results. Our approach permits the estimation of differentconvergence rates to different steady states for each cross sectional unit.When this diversity is allowed, we find that convergence of each unit to(its own) steady state income level is much faster than previously estimatedbut that cross sectional differences persist: inequalities will only bereduced by a small amount by the passage of time. The cross countrydistribution of the steady state is largely explained by the cross countrydistribution of initial conditions.

Educational opportunity and the college premium

Since World War II, the United States government has made improved accessto higher education a priority. This e¤ort has substantially increasedthe number of people who complete college. We show that by reducing theeffective interest rate on borrowing for education, such policies canactually increase the gap in wages between those with a college educationand those without. The mechanism that drives our results is the signaling role of education first explored by Spence (1973). We argue that financialconstraints on education reduce the value of education as a signal. Wesolve for the reduced form relationship between the interest rate and thewage premium in the steady state of a dynamic asymmetric information model.In addition, we discuss evidence of decreases in borrowing costs for educationfinancing in the U.S.

Endogenous business cycles and stabilization policies

The paper reports results on the effects of stylized stabilization policies on endogenously created fluctuations. A simple monetary model with intertemporally optimizing agents is considered. Fluctuations in output may occur due to fluctuations in labor supply which are again caused by volatile expectations which are ``self fulfilling'', i.e. correct given the model. It turns out that stabilization policies that are sufficiently countercyclical in the sense that government spending (on transfers or demand) depends sufficiently strongly negatively on GNP-increases can stabilize the economy at a monetary steadystate for an arbitrarily low degree of distortion of that steady state. Such stabilization has unambiguously good welfare effects and can be achieved without features such as positive lump sum taxation or negative income taxation as part of the stabilization policy.

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.