Perfect multicollinearity (???????)

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??????????????

• 1.???????
• 2.??????????
• 3.??????????
• 4.????

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1.???????

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1.???????

• Perfect multicollinearity (???????)

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????????

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• ????147??(11.2)?????

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??????(Variance-Inflating Factor, VIF)
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??????????????
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2.??????????(p.149)

• (1) High R2 but few significant t ratios.
• (2) High pair-wise correlations among regressors.
• (3) Examination of partial correlations.
• (4) Auxiliary regressions.
• (5) Eigenvalue and condition index.
• (6) Tolerance and variance inflation factor.

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(1) High R2 but few significant t ratios

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(2)????????

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• (Gujarati 1995, 335)
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(3)?????

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(4) ??????

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• ????R2
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• ???R2??????????R2

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(5) ????????

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• ??30????????

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(6)??????????

• VIF??10??????0.949
• TOL1/VIF
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• ??0????????????

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3.??????????

• (1) Large Variances of OLS Estimators
• (2) Wider Confidence Intervals
• (3) Insignificant t Ratio
• (4) A High R2 but Few Significant t Ratio
• (5) Sensitivity of OLS estimators and their
  standard errors to small changes in data

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4.????

• (1). A priori information
• (2). Combining cross-sectional and time series
  data
• (3). Dropping a variable(s) and specification
  bias
• (4). Transformation of variables
• (5). Additional or new data.
• (6). Reducing collinearity in polynomial
  regressions
• (7). Other methodsFactor analysis or principal
  components

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(1)????

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• (Gujarati 1995, 340)

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(2)?????????

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• (??????????????????)

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(3)??????

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• (Model Under-specification)

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(4)????

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(5)??????

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(6)polynomial regressions

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(7)????

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?????????

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• 2.??
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• 4.????
• 5.????

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1.??

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1.????????
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1.?????????
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2.??????????

• As people learn
• The variances of error terms are positively
  correlated with the independent variables.
• When our data collecting techniques improve
• Heteroskedasticity can also arise as a result of
  outliers in our data.
• Another resource of heteroscedasticity arises
  from mis-specifying the regression model.

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(1)????,????
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(2) ??????????

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(3)?????????
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(4)???????
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(5)??????

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3.??????

• 1). Heteroskedasticity, Unbiasedness, and
  Consistency
• 2). Heteroskedasticity and Standard Errors of OLS
  Coefficients
•  The consequences of heteroskedasticity are that
  b is still unbiased and consistent, but its
  variance will be incorrect. In other words, it is
  inefficient.
• Additionally, our conventional test statistics
  are invalid.

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4.????

• ???????
• 1) The White Test
• 2) The Breusch-Pagan-Godfrey Test

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????The White Test

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• (Gujarati 1995,379-80)
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5.????

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?????????(??)

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• 2.??
• 3.??????
• 4.????
• 5.????

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???????(??)
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1.??

• The term autocorrelation (or serial
  correlation) may be defined as correlation
  between members of series of observations ordered
  in time as in time series data or space as in
  cross-sectional data (Gujarati 1995 400-1).

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2.??

• However, serial correlation could indeed be error
  autocorrelation, but it could also be the result
  of dynamic misspecification, parameter
  nonconstancy, incorrect functional form, and so
  on (Granato 1991 124).

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2.??

• According to Kennedy (1992 119), there are
  several reasons why serial correlation arises
• Spatial autocorrelation
• Prolonged influence of shocks
• Inertia
• Data manipulation
• Misspecification

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3.??????

• (1).No Lagged Endogenous Variable
• (2).Lagged Endogenous Variable

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(1).No Lagged Endogenous Variable

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(2).Lagged Endogenous Variable

• ?OLS?????Inconsistent

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4.????

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5.????

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?7???

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