Question

This question asks how certain concepts. Two concepts are
(A) The economic model
(B) The statistical model
Please describe which concepts are used for each of the following purposes. Your answers may be: neither; A; B; or A and B.

i. Defining the OLS estimator.
ii. Defining what we are interested in, such as a specific question: how will wage change if education increases by 1 year, holding everything else fixed.
iii. Concluding that the OLS slope coefficient is a consistent estimator of ˜ β1.
iv. Concluding that if we regress Y on X, the slope coefficient consistently estimates Cov(X,Y )/Var(X).
v. Determining whether to regress Y on X or X on Y .

Answer 1

i. (B): We need to use the statistical model to define the OLS estimator, because the statistical model only determines which estimator to use. The best estimator is the estimator which is unbiased and which has minimum variance out of all the estimators.

ii. (A and B): For defining what we are interested in, we need economic model. In case of example given in the question, we need both economic as well as statistical model. Because, we need Economic model to know the relationship between wage and education levels. After that to check how the wages are changing based on the education, we need statistical model.

iii. (B): We need statistical model to conclude that the OLS slope coefficient is a consistent estimator of β1, because we cannot conclude it by using economic model.

iv. (B): We need statistical model to conclude that if we regress Y on X, the slope coefficient consistently estimates Cov (X, Y)/Var (X), because we cannot do it by using economic model.

v. (A): For determining whether to regress Y on X or X on Y, we need economic model. Because we need to have prior knowledge of economic theory to decide whether to regress Y on X or X on Y, otherwise there will be no meaning in doing regression.