# 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 varia

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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 being linear.

In such cases an auto-regression model is used for forecast

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## Question number: 9

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

Where and are the fixed price and µ be the individual fixed income.

### Explanation

For consumer’s equilibrium, we have

and hence, we get

………………. (i)

since, µ the individual income is fixed, we have

Substituting the value of in (i), we get

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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

with

and with

, ,

and

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

increases, 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 not significantly different from zero

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## Question number: 11

» Econometrics » Autoregressive Linear Regression

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

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

### Explanation

It is given that

……………. (i)

using (i)

Similarly, we will get

But From (i)

Hence,

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