PS11tables

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Problem

Consequences

Test

Correction

Omitted Variable- The omission of a relevant independent variable (data)

Bias in the coefficient estimates

Include the left out variable as a proxy

Decreased precision in the form of lower R² value, higher standard errors, and lower t-scores

1.theory

2 .t-test on B

3.R²

4.Impact on other coefficients if X is dropped

Delete the variable if its inclusion is not required by the underlying theory

Incorrect Functional Form (data)

Biased and inconsistent estimates, poor fit, and difficult interpretation

Examine the theory carefully; think about the relationship between X and Y

Errors in Variables (data)

Biased and/or inefficient estimates

Houseman test

Instrumental variables

Multicollinearity - Some of the independent variables are imprefectly correlated (population)

No biased coefficients but estimates of the separate effects of the Xs are not reliable, ie. High SE’s and low t scores

Drop redundant variables, use combination variable

Simultataneous Equation Bias (population)

Theory/ Test for indentification problem - check numbers of endogeneous and exogeneous variables

Use an alternative to OLS - ie Two Stage Least Squares

Autocorrelation- The error terms for different observations are correlated (population)

No biased coefficients but the variances of the coefficients and t scores fall in a way not captured by OLS

Use Durbin Watson d test, if significantly less than 2, positive serial correlation

Add the ommited variable or change the functional form, consider generalized least squares

Heterosketasticity- The variance of the error terms is not constant for all observations (pop)

Plot the spread or contraction of the residuals or use the Park or Goldfeld Quandt tests

Add the omitted variable. Otherwise, redefine the variables or apply a weighted least squares corr.

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Problem	Consequences	Test	Correction
Omitted Variable- The omission of a relevant independent variable (data)	Bias in the coefficient estimates		Include the left out variable as a proxy
	Decreased precision in the form of lower R² value, higher standard errors, and lower t-scores	1.theory 2 .t-test on B 3.R² 4.Impact on other coefficients if X is dropped	Delete the variable if its inclusion is not required by the underlying theory
Incorrect Functional Form (data)	Biased and inconsistent estimates, poor fit, and difficult interpretation	Examine the theory carefully; think about the relationship between X and Y
Errors in Variables (data)	Biased and/or inefficient estimates	Houseman test	Instrumental variables
Multicollinearity - Some of the independent variables are imprefectly correlated (population)	No biased coefficients but estimates of the separate effects of the Xs are not reliable, ie. High SE’s and low t scores		Drop redundant variables, use combination variable
Simultataneous Equation Bias (population)		Theory/ Test for indentification problem - check numbers of endogeneous and exogeneous variables	Use an alternative to OLS - ie Two Stage Least Squares
Autocorrelation- The error terms for different observations are correlated (population)	No biased coefficients but the variances of the coefficients and t scores fall in a way not captured by OLS	Use Durbin Watson d test, if significantly less than 2, positive serial correlation	Add the ommited variable or change the functional form, consider generalized least squares
Heterosketasticity- The variance of the error terms is not constant for all observations (pop)		Plot the spread or contraction of the residuals or use the Park or Goldfeld Quandt tests	Add the omitted variable. Otherwise, redefine the variables or apply a weighted least squares corr.