Use of dami variables in econometrics

Dami variables

Definition:

“In regression analysis it frequently happen that dependent variable is not only influenced by variables which can be quantified (Cal in NO) on some well known scale like income, output, price and height but also those variables which are qualitative in nature like gender, race, color ,religion , war and peace”

Explanation:

Since such qualitative variables usually indicate the presence and absence of a quality or attribute such as

Male or Female Black and white

One method of identifying by such attribute by constructing artificial variables which take of value

0 indicating the absence of an attribute 1 indicating the presence of an attribute

Exp:0 May indicate the person is female1 May indicate the person is Male

Multi co linearity

Questions

1. What do you understand by multicolenearty? Or explain the nature of multicolenearty.

2. Discuss the consequences of multicolenearty.3. How it can be detected?4. What are the remedial measures?

Answers

1. What do you understand by multicolenearty? Or explain the nature of multicolenearty.

Ans:One of the assumption of classical multiple regression model is that “There exists no exact relationship b/w independent variable in the model if such relationship exists we say the independent variables are perfectly collinear or perfect co linearity is said to exist.

Exp:

Suppose the H- school grades of student depends upon the following variables Y = the grade of the studentX2 = Family incomeX3 = No of hour of study per day X4 = the no of hours of study per week

So model that can be estimate is

Y = 1+2X2+3X3+4X4+Є

In this case variable X3 and X4 are perfectly collinear because

7X3=X4This gives rise to perfect colinearity in model therefore OLS estimates (1, 2, 3) of this model are not possible. Interpretation of 2, 3 are not possible.

2. Discuss the consequences of multicolenearty.

Consequences of multicolenearty

Whenever there is a problem of multicolenearty the variance of the estimated coefficient will be very high.

Exp: variance of 2, 3 will be very big in No.

Interpretation of individual coefficient is of doubtful value Exp:

The value of t coefficients is very small but the value R2 is very high.

Note:For Significance check T-Test For Importance R2

For Overall goodness of model K-Test

3. How it can be detected?

Detection of multicolenearty

If simple co relation coefficient b/w two independent variable is higher than the practical co relation or multiple co- relation then it is a problem of multicolenearty.

r > Rr = simple co relationship

R = Partial

4. What are the remedial measures?

It depends upon the objective of the model 2 main objectives

For casting Structural analysis

If we take structural measure then increase the sample size.

Heteroskedasticity

Questions

1. What is the nature of Heteroskedasticity& what do you understand by heteroskedasticity?

2. Major causes of heteroskedasticity3. How it can be detected 4. Remedial measure of hetro

Introduction

If all the assumptions of OLS are satisfied the OLS estimates are blue. However if anyone of assumption is violated the estimates are no more blue.Violation of the assumptions regarding variance of error term has very serious problems.

Regards, heteroskedasticity the above questions will be answered

1. What is the nature of Heteroskedasticity& what do you understand by heteroskedasticity?

One of the important assumptions of OLS is that The variance of each of the ε (error term) is constant

Variance of (ε) =

But if the variance is not constant then the problem of hetro is said to be present

Variance of (ε) =

2. Major causes of heteroskedasticity

It is expected in cross sectional data As data collection technique changes, variance also changes that cause hetro

Major consequences of Hetro (Very Important Regarding Paper Point of View)

1. In the presence of hetro the blue estimates are no more bestOr The estimates are still unbiased but they are no more best or efficient 2. The variance of the estimated errors are bigger than decase such Case)Or Hetro variance will be bigger when there is no hetro3. In case of hetro the usual test like T-test, F-test etc will provide the misleading

resultsFor exp:

if variance of ^2 is bigger because of hetro then S.E of ^2 will also bigger when S.E is bigger then the value of t will be smaller and that situation you fail to reject H0

Method of detection of Hetro Graphical Mathematical

Graphical In this method we plot the square of error against time. And by inspection we can determine whether hetro is present or not

Mathematical method

1. Gould feld quant test 2. Spilled man rank correlation test 3. Park glejser Test for heteroskedasticity

t = ^2 / S.E (^2)

Splid man rank correlation test for heteroskedasticity

This test is based upon the following steps

1. Fit the regression of Y on X and obtain residual 2. ignore the sign of residual and then rank both independent variable X and residual

according to ascending order or descending order and compute the Splid man correlation denoted by rs

Where d is the difference of two ranks and n is the sample size

3. Test Ho by t-test

t = rs (n-2)

(1- rs2)

with n-2 degree of freedom

4. if t is significant mean tcal > ttab reject Ho other wise fail to reject

Example

rs = 1-6 [Σ di2 / n (n2-1) ]

Park glejser Test for heteroskedasticity

This test tells us that how to correct heteroskedasticity

There are two main objectives

Tells id there is hetro or nor It makes correction for hetro

Є = +X+Є

If and are insignificant stop and conclude about the absence of hetro

But if is significant tcal > ttab then we have to take following steps

1. transform the original variables into new

= Σ x*y* Σx*2

= Y - X

Y* = Y / XX* = 1 / X

Є* = Є/X

Standardize equation

Y* = + X* + Є*