# Note7 - 1 Threats to Internal Validity Violations of Gauss-Markov Threats to Internal Validity 1 Poorly estimated standard errors a

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Threats to Internal Validity, Violations of Gauss-Markov Threats to Internal Validity 1. Poorly estimated standard errors. a. Hetroskedasticity, violate assumption A3 b. Autocorrelation, violate assumption A4 2. Correlated regressors and their error terms. a. Omitted Variables Bias, violate assumption A5 b. Mis-specified Model, violate assumption A5 c. Errors in Variables, violate assumption A5 d. Sample selection, violate assumption A5 e. Simultaneous equations, assumption A5 I. Omitted Variables Bias a. Problem: a variable that determines the dependent variable and is correlated with one of the independent variables is omitted. b. Consequence: Bias and inconsistent asymptotically. c. Solution: i. Include the omitted variable ii. Include a proxy for the omitted variable d. Detecting omitted variables bias i. If the possibly omitted variable is available, do existing regression coefficients change appreciably when the variable in question is omitted? 1. if yes, the variable in question should remain in the model. 1

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2. if no, the variable in question can be left out of the model. ii. If the omitted variable is not observed 1. use data in which the same observation unit is observed at different points in time. This is valid only if the omitted variable does not change over time. 2. instrumental variables regression 3. randomized and controlled experiment II. Mis-specified model a. Definition: The functional form of the estimated regression function differs from the functional form of the population regression function. This mis-specification creates omitted variable bias. b. Detection i. Graph and look at the pattern. If modeled as a linear model, is there an apparent non-linear form to the model? ii. Durbin-Watson statistic iii. RESET test. Reset test is not an omitted variables test, only to the extent a polynomial or other transformation variable is omitted; it is a mis-specified model test. III. Errors in variables test a. Definition: Errors in variables results because there is measured error in a dependent variable b. Sources of Measurement error i i i x x ε + = ~ 2
where x ~ is the dependent variable measured with error ] ) ~ ( [ ~ ε β α + - + + = x x x y i η + + = x y ~ where + - = ) ~ ( x x i c. If the difference between the actual and observed independent variable, ( 29 , ~ i i x x - is correlated with the measured value, x ~ , then the regressor with be correlated with the error term and β will be biased and inconsistent, i.e., measurement error creates omitted variables bias. σ 2 2 2 ˆ w x x + → Because the ratio, 2 2 2 w x x + , is less than one, ˆ , has a downward bias. This leads to what has come to be known as Hausman’s Law of Measurement error, which is to say that because of errors in measurement that slope coefficients inevitably have a downward bias.

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## This note was uploaded on 08/06/2009 for the course ECON 140 taught by Professor Duncan during the Spring '08 term at University of California, Berkeley.

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Note7 - 1 Threats to Internal Validity Violations of Gauss-Markov Threats to Internal Validity 1 Poorly estimated standard errors a

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