所屬科目：統計學
(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 +B1Xi + 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 modelLet be the OLS estimator ofβ1based on the available sample. Suppose that the i'thobservation is included in the sample only ifthen is consistent.
(d) (5%) In the context of a controlled experiment, consider the simple linear regression model , where Yi is the outcome, Xi 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 Xi 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?
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Definition 1 For an estimator
is a sequence of
constants (a normalizing constant), then τ2 is called the limiting variance.
State clearly what theorems/ properties you use.
be the OLS estimator ofβ1based on the available sample. Suppose that the i'th
, where Yi is the outcome, Xi 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.
. Suppose that Xi is measured with error, and the measured 
is independent of X with variance
using OIS, what is the probability limit of 
?
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
in (b) greater or smaller than the bias of 
in (a)?