Monte-Carlo Simulations can help one prove the minimum variance property of OLS betasa.Nob.Yes

We use ------to derive the OLS betasa.Derivative and sum of residualsb.Sum of squared residualsc.Derivatived.Derivative and sum of squared residuals

pset 5.2 Prove that $\hat{\boldsymbol{\beta}}_{G I V E}$ can be derived as the OLS estimator of $\boldsymbol{\beta}$ in the linear regression model$$\boldsymbol{y}=X \boldsymbol{\beta}+\hat{U} \boldsymbol{\gamma}+\boldsymbol{\eta}$$where $\hat{U}$ is the matrix of first-stage residuals.

pset 6.1 Prove that the OLS estimator of $\boldsymbol{\beta}$ in the linear regression model with individualspecific intercepts, that is$$y_{i t}=\boldsymbol{x}_{i t}^{\prime} \boldsymbol{\beta}+\alpha_{i}+u_{i t},$$where $\alpha_{i}$ is a parameter to be estimated, for $i=1, \ldots, n$ is equal to $\hat{\boldsymbol{\beta}}_{W G}$.

The variance of the OLS estimatorQuestion 1Select one:a.increases as the number of observations increasesb.increases as the variance of the unobservable increasesc.decreases as the number of observations increasesd.decreases as the variance of the unobservable increasese.a) and b) are truef.b) and c) are trueg.c) and d) are true

The variance of the OLS estimatorchoose the right option(s):O a.increases as the number of observations increaseso b.increases as the variance of the unobservable increasesoc.decreases as the number of observations increases d.decreases as the variance of the unobservable increases