DUMMY VARIABLE REGRESSION MODELS

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DUMMY VARIABLE REGRESSION MODELS

• Lecture week 3
• Prepared by
• Dr. Zerihun Gudeta

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INTRODUCTION

• Quantitative versus qualitative variables.
• Quantifying qualitative variables in regression
  Analysis.
• Purpose of dummy variables in regression
  analysis statistical differences in averages,
  statistical differences in slopes, interaction
  effects, structural break, seasonal analysis,
  etc.
• Dummy regressor models ANOVA (exclusively
  dummy), ANCOVA (dummy and quantitative
  variables).

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Use of dummy variables to test for changes on
averages ANOVA

• Objective comparing average agricultural output
  collected from various farms under various levels
  of chemical fertilizer and pesticides
  application.
• Problem quantification of fertilizer and
  pesticides application.
• Three categories optimum application of both,
  application of either fertilizer or pesticides,
  and application of none of the inputs. Consider
  optimum application of both as the base category.

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Use of dummy variables to test for statistical
changes for averages ANOVA (cont)

• The equations

Test for significance differences in average
yields check whether a3 is significantly
different from zero to see whether a0 ? a0 a3.
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Use of dummy variables to test changes for
averages ANOVA example
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Use of dummies to test for significant changes in
slopes

• Regression with qualitative and quantitative
  variable
• Earning (y) a function of education (E), gender
  (G), experience X
• Testable hypothesis
• Gender has positive effect on earnings i.e. males
  earn more than females.
• Gender influences earnings not only directly, but
  also indirectly by modifying the returns to
  education.
• The function
• Y f(E,G,X,X2)
• lnY ? ?1E ?X ?X2 ?1G ?2GE ?
• G 1 if male, 0 otherwise
• PRF for male
• E(lnY E, X, X2, G 1) (? ?1) (?1 ?2)E
  ?X ?X2
• PRF for female
• E(lnY E, X, X2, G 0) ? ?1E ?X ?X2 ?

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Use of dummies to test for significant changes in
slopes

• PRF for male E(lnY E, X, X2, G 1) (?
  ?1) (?1 ?2)E ?X ?X2
• PRF for female E(lnY E, X, X2, G 0) ?
  ?1E ?X ?X2 ?
• Test Males earn more than females, gender
  affects returns to education
• test that (? ?1) ?
• Check for the statistical significance of ?1
• Test that (?1 ?2) ?1
• Check for the statistical significance of ?2

PRF for males if ?1?0 ?2 ?0
Earning
PRF for males if ?1?0 ?2 0
PRF for females
? ?1
?
Experience
0
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Use of dummies to create interaction dummies

• Regression with qualitative and quantitative
  variable
• Earning (y) a function of education (E), gender
  (G), experience X and race R. Race has four
  categories black, white, coloured, and Indian.
  Only three dummies i.e. black, coloured and
  Indian are used and white is considered as a base
  category.
• The equation
• lnY ? ?1E ?X ?X2 ?1G ?2AF ?3CO
  ?4IN ?
• Variable def AF 1 if African, 0 otherwise.
  Same with other race dummies
• PRF for African male
• E(lnYE,X,X2,G1,AF1, CO0,IN0) (? ?1
  ?2) ?E ?X ?X2
• The assumption the differential effect of gender
  is the same across race. The differential effect
  of race is constant across gender.
• The problem does not help to test income
  disparities say between African men and women,
  between African women and Indian women, etc
• Solution introduce interaction dummy by
  multiplying gender dummy with race dummy.

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Use of dummy variables in place of the Chow
test to test for structural stability

• Objective we want to study the relationship
  between farm income and saving using 26 years
  historical data on farm income and saving
  obtained from a hypothetical farm.
• Problem there was a policy change which occurred
  in 1981 which affected farmers guaranteed access
  to market as a result of the introduction of
  market liberalization.
• Implication of the problem to econometric
  modelling using OLS using the data as it is may
  result in the violation of OLS assumptions
  (consistence of parameters i.e. the Lucas
  critique).
• Solutions Apply econometric technique to decide
  whether the two data sets should be pooled or
  that the relationship between income and savings
  be estimated for the two periods separately.

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Use of dummy variables .

• Available econometric techniques the chow test
  and use of dummy variables.
• Next we see the advantages of using a dummy
  variable over the chow test to test for
  structural stability. But first we see how the
  chow test can be applied to test for structural
  stability using the formula you already know and
  E-views program.

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The chow test

• Two samples the period before 1982 (1970 -1981)
  the period after 1982 (1982 -1995).
• Problem whether to pool or not to pool the data
  and estimate regression equation for 1970-1995.
• The equations

Steps followed to test the null that there is
parameter stability
1.Obtain Residual Sum of Square Estimates (RSS)
from samples 1, 2 and 3. 2. Sum RSS obtained from
sample 1 2 to obtain Unrestricted Residual Sum
of Squares (RSSUR) with degree of freedom (df)
equal to sum of sub sample observations minus sum
of number of parameter estimated in Tables 1 and
2. 3. Call RSS obtained from sample 3 Restricted
RSS (RSSR). 4. Form the null-hypothesis i.e. no
structural change or sample 1 and 2 are the
same. 5. Calculate F-statistic as
6.Make decision compare critical value with
calculated F. Accept the null for parameter
stability if calculated F value is less than
critical value other wise do not accept the null.
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Chow test (cont)

• Error terms in the sub-period regressions are
  normally distributed with the same variance and
  that the error terms are independently
  distributed.
• Do this assumptions hold? If they do not, this
  implies that we should not use the chow test for
  the type of example we have.
• The null hypothesis we should test is that the
  variance of the two subpopulations are the same.
• Information that we do not get from the Chow test
• Failure to test the validity of equal variance
  assumption cast doubt on the validity of our
  conclusion.

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Solution to problem posed by Chow Test

• Use dummy variables as an alternative to the Chow
  test. The method is easy to apply. It can be done
  by fitting only one equation (no need of fitting
  three or more equations like the Chow test)
  possible changes in the variance of error terms
  may be handled with the introduction of intercept
  and/or slope dummies in the equation and unlike
  the Chow test, the effect of the structural break
  on the slope or intercept coefficient can be
  easily determined.
• Specification of the model

• Where Dum is intercept dummy. It is included
  in the equation to measure the effect of
• the structural break on the intercept of
  the equation. It takes a value of 0 for
• observations between 1970 and 1981and 1 for
  observations between 1982 and 1995.
• IncomeDum is slope dummy. It measures the
  effect of the structural break on the slope
• of the equation.