An Investigation of the Pay-As-You-Go Financing Method Using a Contingency Fund and Optimal Control Techniques

In many countries, aging populations are expected to lead to substantial rises in the cost of public pension systems financed by the pay-as-you-go (PAYGO) method. These systems will need to be adapted to cope with these changes. This paper considers one approach to reform, described in the literature as “parametric” (see, e.g., Disney 2000), and develops a model for adapting the PAYGO method using a contingency fund and optimal control techniques. The solution of the original model is investigated within two different frameworks: a deterministic-continuous one and a stochastic-discrete one. Finally, a case study applied to Greece is discussed, leading to a potentially acceptable proposal of a smooth path for contribution rates and the age of eligibility for the normal retirement pension

Illuminating growth and struggles using mixed methods: Practice-based professional development and coaching for differentiating SRSD instruction in writing

In this mixed methods study, qualitative, quantitative, and single-case methods were combined to provide a comprehensive investigation of teacher and student outcomes following practice-based professional development (PBPD) for self-regulated strategy development (SRSD) in writing. Qualitative observations were used to determine outcomes among the three-fourth grade teachers involved, a nested quantitative model was used to analyze classwide student writing outcomes across 53 students in the three classes, and single case design was used to determine differential outcomes among randomly selected struggling and average writers in each class. PBPD was followed by coaching for differentiation based on student performance and fidelity as teachers taught their students strategies for writing timed imaginary stories (with self as main character), as required by the state writing test. Qualitative results indicated two teachers did not differentiate writing instruction without coaching; one teacher was unresponsive to coaching and did not differentiate instruction. Classwide analysis demonstrated significant growth in writing at the class level for students from baseline to posttesting. Single case design results indicated mixed outcomes among struggling and average writers and instances where instruction was not effective. Teachers indicated high social validity for PBPD and for SRSD; students indicated high social validity for SRSD. Results across the multiple methods illuminate growth and struggles often disguised in group data and are addressed to aid in understanding and enhancing PBPD as well as instruction in SRSD and other evidence-based practices. Limitations and future research directions are discussed