110年 - 110 國立臺灣大學_碩士班招生考試_經濟學研究所：統計學（A）#105677

(a) Find Cov

(c) Consider the following estimator of θ:Definition 1 For an estimatoris a sequence of constants (a normalizing constant), then τ² is called the limiting variance.

(d) Find the optimal choice of c that minimizes the limiting variance of  State clearly what theorems/ properties you use.

(a) Describe how to apply the inverse method to generate Logistic random variables X, with pdf:
 

(a) What is the impact of 1% increase in export growth on GDP growth for countries with a fixed exchange rate regime (ie, fixers)? Now suppose the empirical results are as follows:
where standard errors are in parentheses.

(b) (5%) In a linear probability model, Yi=βo +B₁X_i + ui, where Yi is a binary variable and takes the value of o or 1, the OLS estimate of β₁ is consistent and efficient.

(c) (5%) For the model

Let be the OLS estimator ofβ₁based on the available sample. Suppose that the i'th
observation is included in the sample only if
then  is consistent.

(d) (5%) In the context of a controlled experiment, consider the simple linear regression model , where Y_i is the outcome, X_i is the randomly assigned treatment level, and u: contains all the additional determinants of the outcome. Then the OLS estimator of B will be inconsistent since there are omitted variables present.

(a) (4%) Consider the bivariate regression model,. Suppose that X_i is measured with error, and the measured is independent of X with variance using OIS, what is the probability limit of ?

(b) (7%) Consider the bivariate regression model with two-period panel data, where are correlated with correlation coefficient px ＞ o. Suppose that X, is measured with error, and the measured Xi, is Xi. = Xis t wis where Wil is not autocorrelated and is independent of on

(c) (4%) Is the bias of in (b) greater or smaller than the bias of in (a)?

(a) (5%) Is the OLS estimate of β₁ consistent? Why?