This assignment solution delves into key statistical concepts, beginning with an explanation of sampling distributions, emphasizing their theoretical nature and the process of obtaining them through random sampling from a population. It highlights the desired characteristics of an estimator, focusing on unbiasedness and consideration of sampling variability. The solution then explores the fixed effects method in detail, outlining its role in reducing bias by controlling stable characteristics and within-person variation, while acknowledging its limitations regarding between-person variation. Finally, it examines the method of instrumental variables, explaining its use in estimating causal relationships when controlled experiments are not feasible, and discussing its application in addressing issues like variable omission and measurement error in OLS regression, providing an example of its use in addressing ability bias in education return analysis.