Econometrics (ISS (Statistical Services) Statistics Paper III): Questions 7  11 of 21
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Question number: 7
» Econometrics » AutoCorrelation
Appeared in Year: 2009
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
Question number: 8
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2011
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 t1, t2, …, tk, the relationship
Question number: 9
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2011
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),
Question number: 10
» Econometrics » AutoCorrelation
Appeared in Year: 2011
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:

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

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
Question number: 11
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2011
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,
From (i)
Auto correlation of order k is
, which is independent of k.
Hence, the process is stationary