Econometrics (ISS (Statistical Services) Statistics Paper III): Questions 7 - 11 of 21

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Question number: 7

» Econometrics » Auto-Correlation

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Define multicollinearity. What are the causes of multicollinearity? How will you detect the same and solve it?

Explanation

Multicollinearity: Implies predictors that are correlated with other predictors in the model. Here two or more predictor variables in a multiple regression model are highly correlated and implies that one can be linearly predicted from the others with a substantial degree of accuracy.

Causes of multicollinearity:

  • Inaccurate use of dummy

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Question number: 8

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Discuss second order autoregressive series. For this series, obtain complementary function (CF) only.

Explanation

Second order autoregressive series:

Sometimes, the values of a time series data are highly correlated with the values that precede and succeed them. i. e. , The value of a time series at any time “t” may depend upon its own value at times t-1, t-2, …, t-k, the relationship

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Question number: 9

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2011

Essay Question▾

Describe in Detail

If Equation is an individual’s utility function of two goods, show that the demand for the goods is Equation and Equation

WhereEquation and Equation are the fixed price and µ be the individual fixed income.

Explanation

For consumer’s equilibrium, we have

Equation

Equation and hence, we get

Equation

Equation

Equation

Equation

Equation

Equation

Equation ………………. (i)

since, µ the individual income is fixed, we have

Equation

Equation

Equation

Substituting the value of Equation in (i),

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Question number: 10

» Econometrics » Auto-Correlation

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Discuss the effect of imperfect multicollinearity on tests and errors. Consider a model

Equation with

Equation and Equation with

Equation , Equation , Equation

and Equation

Do you think multicollinearity is present in the model? If yes, give reasons. Further show that as

Equation increases, Equation also increases.

Explanation

Effect of imperfect multicollinearity on tests and errors:

  1. OLS estimators will be BLUE, but they have large variances and covariances. this makes the estimation difficult.

  2. The confidence intervals will be wider. and hence, we may not reject the ’zero null hypothesis i. e. , We may conclude that B’s are

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Question number: 11

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Equation , - ∞ < t < ∞, where Equation are i, i. d. with Equation and Equation . Show that the process is stationary with correlation.

Explanation

It is given that Equation

Equation ……………. (i)

Equation

Equation

Equation using (i)

Similarly, we will get

Equation

Equation

But Equation From (i)

Hence, Equation

Equation

Equation Equation

Equation From (i)

Auto -correlation of order k is

Equation , which is independent of k.

Hence, the process is stationary

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