Multicollinearity

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Multicollinearity

• Correlation among the independent variables

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Multicollinearity
Y
X
Z
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Exact Multicollinearity

• ZabX
• Regression model YabXgZe
• The two normal equations are not independent and
  reduce to the same equation
• Use multicol1.dta to estimate equation above

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General Points

• Perfect multicollinearity is rare
• Economic variables will almost always have some
  correlation with one another.
• The question is whether the multicollinearity is
  so severe as to alter the estimation of the
  coefficients.
• Multicollinearity is frequently both a
  theoretical problem and problem with a particular
  sample of data.

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Consequences

• Estimates will remain unbiased
• The variances of the estimates will increase
• Computed t-scores will fall

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Consequences

• Estimates will become very sensitive to changes
  in specification
• The overall fit of the equation will be
  unaffected
• The estimation of the variables that are not
  collinear will be unaffected

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Detection

• High R Squared with all low t-scores
• High simple correlation coefficients
• Coefficients sensitive to specfication
• Formal tests

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Toyota
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Detection

• Unexpected sign on miles
• Correlation coefficient 0.995
• Coefficients sensitive to specification

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Remedies

• Do nothing
• Drop a variable
• Incorporate more information
• More data
• Formalize Relationships among regressors
• Specify relationships among parameters
• Create a composite variable

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Alternative Specifications
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LA Apartment Rents
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Detection and Remedies

• Unexpected Sign on Number of Bedrooms
• Insignificant Coefficient
• Correlation between bedrooms and square footage
  .81
• Remedy -- drop bedroom. Adjusted R Square
  increases.

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Housing Starts
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Detection

• Unexpected signs
• Low t-stats
• High pairwise correlations between LGNP and LPOP
  and between LINTR and LGNP and between LINTR and
  LUEMP.

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Correlation Matrix
lgnp lintr lpop
lunemp ------------------------------------------
-- lgnp 1.0000 lintr 0.9185
1.0000 lpop 0.9882 0.9458 1.0000
lunemp 0.6906 0.7681 0.7778 1.0000
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Remedies

• Drop LPOP and LUEMP
• Do nothing about correlation between LINTR and
  LGNP

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Final Words

• Dont go looking for multicollinearity. Almost
  all economic data is correlated so you can
  usually find it. It is only a problem in so far
  as it affects your results.