Endogeneity

What are the 4 reasons endogeneity may arise

1. Omitted variable bias: the variations in x and in y may be due to another variable which is unobserved 2. Measurement error: the data may only provide an inaccurate measure of x 3. Simultaneity bias: variations in x may be themselves triggered by variations in y so causality runs both ways 4. Selection bias: y or x may be observed only for a selected sample of individuals, depending on unobserved characteristics

Correlation

A measure of the relationship between two variables

In order for βˆ 1 to be a consistent estimator for β1 when there is a measurement error in the dependent variable, what must be true

E(xi(ui + ei)) = E(xiui) + E(xiei) = 0

endogenous

If an explanatory variable is correlated with the error term (i.e., the exogeneity assumption does not hold) ⇒ OLS estimator is: 1) biased: E(βˆ1) not equal to β1 2) inconsistent: the bias persists in large samples

exogenous

If an explanatory variable is not correlated with the error term

What does it mean if we have a measurement error

If one or more relevant regressors is measured with some error, then the OLS estimator is biased in finite samples The bias persists in large samples, i.e., OLS estimator is inconsistent.

Is mismeasuring the dependent variable problamatic

In general, mismeasuring the dependent variable is unproblematic, as long as this measurement error is uncorrelated with the regressors

How can we prove inconsistency in the classical errors in variables

The magnitude of this bias varies according to the magnitude of σ 2 e , i.e., the dispersion of measurement error

What is a casual relationship

The simple OLS estimator will be E(ui | xi) = 0 as long as the zero conditional mean assumption is present. In the absence of this assumption, two very important properties, unbiasedness and consistency, will no longer hold

What is omitted variable bias?

When the regressor is correlated with a variable that has been omitted from the analysis and that determines in part, the dependent variable. Therefore inconsistent

What is a long regression

When there is another explanatory variable that can be added into the regression but is correlated to another explanatory variable

What is a short regression

When there isnt a correlated explanatory variable included in the regression

Classical-Errors-in-Variables assumption

is that the measurement error is uncorrelated with the unobserved explanatory variable (i.e., E(x∗i ei) = 0 or Cov(x∗ i , ei) = 0)

Causality

the relationship between cause and effect

Internal validity

the statistical inferences about causal effects are valid for the population being studied