Question

Question 3 True/False/Explain 1. The variance of the OLS estimator of the coefficient of a certain variable X; in a regression is higher, the higher is the degree of collinearity between that variable and the other regressors included in the model 2. Suppose that we estimated the following hourly wage equation n(wage) .092educ + .0041ехреr + (007) 022tenure 284 (0017) (.104) (003) where the numbers in parentheses are estimated standard errors. Assuming that the classical normal linear regression model holds, the 90% confidence interval for the coefficient on exper is [.0041 - 1.96 x .0017, .0041 1.96 x .0017 Question 4 Suppose you estimate the consumption function Ү, — Q1 + 02Х, + uji = O1 and the savings function: Z, 3D В + BzX, + uzi where Y consumption, Z = is equal to consumption plus savings. What is the relationship, if any, between a2 and 32, and between a1 and 6? income, and X = Y + Z, that is, income savings, X

Answer 1

Question 3.

1. False, as just by looking at the variance of the OLS estimate of independent variable, it cannot be inferred if there is collinearity between independent variables.

In case of a multiple linear regression model, a measure of collinearity among independent variables is the Variance Inflation Factor that identifies the change in the variance of a particular independent variable X_j when some other independent variable changes. It is not the variance value, but the value of the Variance Inflation Factor that decides the degree of collinearity.

2. For a 90% confidence interval in case of a normal distribution, the z value is 1.645.

In order to calculate the confidence interval, the mean and the standard errors are used as follows :

The confidence interval = [mean - Z * Standard Error, mean + Z * Standard Error] =

[0.0041-1.645* 0.0017, 0.0041+1.645* 0.0017] = [0.0013,0.006897]

Thus, with 90% confidence, the average experience lies between this confidence interval.

Question 4

As income, X = Consumption, Y + Savings, Z,

Here, in the Consumption function, $\alpha$₁ is autonomous consumption and in the Savings function, $\beta$₁ is the negative of  $\alpha$₁ i.e. the autonomous saving ($\beta$₁ = - $\alpha$₁)

On the other hand, $\alpha$₂ is the marginal propensity to consume (The increase in consumption as income increases by one unit) and $\beta$₂ is the marginal propensity to save (The increase in savings as income increases by one unit) which is (1- $\alpha$₂). Thus there is a negative relation between $\beta$₂ and $\alpha$_2.