Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

A recessionary debate: who suffered more? A study of sectoral well-being and economic insecurity in Ireland

The aim of this thesis is to identify the relationship between subjective well-being and economic insecurity for public and private sector workers in Ireland using the European Social Survey 2010-2012. Life satisfaction and job satisfaction are the indicators used to measure subjective well-being. Economic insecurity is approximated by regional unemployment rates and self-perceived job insecurity. Potential sample selection bias and endogeneity bias are accounted for. It is traditionally believed that public sector workers are relatively more protected against insecurity due to very institution of public sector employment. The institution of public sector employment is made up of stricter dismissal practices (Luechinger et al., 2010a) and less volatile employment (Freeman, 1987) where workers are subsequently less likely to be affected by business cycle downturns (Clark and Postal-Vinay, 2009). It is found in the literature that economic insecurity depresses the well-being of public sector workers to a lesser degree than private sector workers (Luechinger et al., 2010a; Artz and Kaya, 2014). These studies provide the rationale for this thesis in testing for similar relationships in an Irish context. Sample selection bias arises when a selection into a particular category is not random (Heckman, 1979). An example of this is non-random selection into public sector employment based on personal characteristics (Heckman, 1979; Luechinger et al., 2010b). If selection into public sector employment is not corrected for this can lead to biased and inconsistent estimators (Gujarati, 2009). Selection bias of public sector employment is corrected for by using a standard Two-Step Heckman Probit OLS estimation method. Following Luechinger et al. (2010b), the propensity for individuals to select into public sector employment is estimated by a binomial probit model with the inclusion of the additional regressor Irish citizenship. Job satisfaction is then estimated by Ordinary Least Squares (OLS) with the inclusion of a sample correction term similar as is done in Clark (1997). Endogeneity is where an independent variable included in the model is determined within in the context of the model (Chenhall and Moers, 2007). The econometric definition states that an endogenous independent variable is one that is correlated with the error term (Wooldridge, 2010). Endogeneity is expected to be present due to a simultaneous relationship between job insecurity and job satisfaction whereby both variables are jointly determined (Theodossiou and Vasileiou, 2007). Simultaneity, as an instigator of endogeneity, is corrected for using Instrumental Variables (IV) techniques. Limited Information Methods and Full Information Methods of estimation of simultaneous equations models are assed and compared. The general results show that job insecurity depresses the subjective well-being of all workers in both the public and private sectors in Ireland. The magnitude of this effect differs among sectoral workers. The subjective well-being of private sector workers is more adversely affected by job insecurity than the subjective well-being of public sector workers. This is observed in basic ordered probit estimations of both a life satisfaction equation and a job satisfaction equation. The marginal effects from the ordered probit estimation of a basic job satisfaction equation show that as job insecurity increases the probability of reporting a 9 on a 10-point job satisfaction scale significantly decreases by 3.4% for the whole sample of workers, 2.8% for public sector workers and 4.0% for private sector workers. Artz and Kaya (2014) explain that as a result of many austerity policies implemented to reduce government expenditure during the economic recession, workers in the public sector may for the first time face worsening perceptions of job security which can have significant implications for their well-being (Artz and Kaya, 2014). This can be observed in the marginal effects where job insecurity negatively impacts the well-being of public sector workers in Ireland. However, in accordance with Luechinger et al. (2010a) the results show that private sector workers are more adversely impacted by economic insecurity than public sector workers. This suggests that in a time of high economic volatility, the institution of public sector employment held and was able to protect workers against some of the well-being consequences of rising insecurity. In estimating the relationship between subjective well-being and economic insecurity advanced econometric issues arise. The results show that when selection bias is corrected for, any statistically significant relationship between job insecurity and job satisfaction disappears for public sector workers. Additionally, in order to correct for endogeneity bias the simultaneous equations model for job satisfaction and job insecurity is estimated by Limited Information and Full Information Methods. The results from two different estimators classified as Limited Information Methods support the general findings of this research. Moreover, the magnitude of the endogeneity-corrected estimates are twice as large as those not corrected for endogeneity bias which is similarly found in Geishecker (2010, 2012). As part of the analysis into the effect of economic insecurity on subjective well-being, the effects of other socioeconomic variables and work-related variables are examined for public and private sector workers in Ireland.

Testing for biases in selection on avian reproductive traits and partitioning direct and indirect selection using quantitative genetic models

Key life history traits such as breeding time and clutch size are frequently both heritable and under directional selection, yet many studies fail to document micro-evolutionary responses. One general explanation is that selection estimates are biased by the omission of correlated traits that have causal effects on fitness, but few valid tests of this exist. Here we show, using a quantitative genetic framework and six decades of life-history data on two free-living populations of great tits Parus major, that selection estimates for egg-laying date and clutch size are relatively unbiased. Predicted responses to selection based on the Robertson-Price Identity were similar to those based on the multivariate breeder’s equation, indicating that unmeasured covarying traits were not missing from the analysis. Changing patterns of phenotypic selection on these traits (for laying date, linked to climate change) therefore reflect changing selection on breeding values, and genetic constraints appear not to limit their independent evolution. Quantitative genetic analysis of correlational data from pedigreed populations can be a valuable complement to experimental approaches to help identify whether apparent associations between traits and fitness are biased by missing traits, and to parse the roles of direct versus indirect selection across a range of environments.