Decided and Undecided Freshmen Majors: Differences on Selected Variables.

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Global existence of dissipative solutions to the Camassa--Holm equation with transport noise

We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for dissipative weak martingale solutions to this SPDE, with general finite-energy initial data. The solution is obtained as the limit of classical solutions to parabolic SPDEs. The proof combines model-specific statistical estimates with stochastic propagation of compactness techniques, along with the systematic use of tightness and a.s. representations of random variables on specific quasi-Polish spaces. The spatial dependence of the noise function makes more difficult the analysis of a priori estimates and various renormalisations, giving rise to nonlinear terms induced by the martingale part of the equation and the second-order Stratonovich--It\^{o} correction term.Comment: 86 page

Estimated Earnings in an Employment Status Model with Banded Data

Introduction: In this paper we consider the estimation of earnings equations for individuals who are either self employed or are in paid employment, and who are assumed to have freely chosen their employment status. The key aspect of the available data is that we do not observe an individual's earnings. Instead we only know in which of several bands an individual's earnings are located. This has implications for the choice of econometric technique and implies that the ordered probit, or the ordered probit with selectivity, are the statistical models that appear most appropriate. Commonly used estimation techniques such as the two-step estimator due to Heckman (1979) are inappropriate. However, there is an important difference between the ordered probit model as defined in this paper and as defined in, for example, Greene (1997). The Greene definition of the ordered probit assumes that the band separations are unknowns to be estimated, whereas they are known in our data set. This situation is not uncharacteristic of survey data where individuals, or firms, are reluctant to disclose their precise income. Knowledge of the band separations implies that the parameters in the earnings equation are identified and can therefore be estimated1. Parameter estimation is discussed in detail in section 2. The data and the economic framework are discussed in section 3. The estimation results are presented and discussed in section 4. Our conclusions are presented in section 5

Potential Entrepeneurs and the Self-Employment Choice Decision

In this paper we estimate, on a dataset for the UK, a standard model of self-employment choice. The model is then extended to allow for differences in the potential for self-employment amongst employees. Specifically, we recognise four relevant groups: actual entrepreneurs, potential entrepreneurs, latent entrepreneurs, and non-entrepreneurs. This hypothesised division allows the incorporation of insights from the sociological and psychological literature on entrepreneurship, as well as the more usual economic and socio-demographic variables. The two models appear reasonably robust on statistical grounds. The predictive performance of the standard and sequential models is similar, although both models tend to under predict the number of self-employed. Nevertheless, we believe that the sequential model offers some distinct advantages over the standard model. In separating out the determinants of interest from the idea and firm formation decisions, the model identifies a set of characteristics that are necessary for start-up i.e. the factors determining interest, but which are not sufficient. In the standard model, the necessary and sufficient conditions are assumed to be identical. The results have implications for policy because they reveal a clear distinction between the factors governing interest in entrepreneurship and those influencing start-up from within the interested group

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments