topic 11 - assessing the validity of the OLS estimators

internal validity, and what conditions does it need to meet

inferences about casual effects are valid for the population being studied, requires OLS estimators to be unbiased and efficient

what determines the efficiency of the OLS estimators

variance - homoscedastiticy

define homoscedastiticy

the dispersion of values of y about the mean are the same for all levels of x : V(yi|xi)=σ²

heteroscedastiticy meaning and implications for OLS

the dispersion of values of y about the mean are different for all levels of x: V(yi|xi)=σ². this is what affects the efficiency of the estimators

how would you detect for heteroscedastiticy

conduct an LM test

steps for LM

estimate the model find ehat i and yhat i, and replace y and xi respectively. find the new R². conduct the LM stat. if LM< Critical value, then reject H0 of homoscedasticity

what are the consequences of heteroscedastiticy

the least squares estimator is still a linear, unbiased estimator but it is not longer the best

the standard errors are now incorrect, need to find the ‘robust’ standard errors

what is required for unbiased/consistent estimators

random sampling, zcm

under zcm what are x

exogenous - uncorrelated

if zcm doesnt hold, what are x and explain how the ols is biased/incosistent

endogenous, there is an endogeneity problem so the OLS estimator is biased. this bias persists even in large samples, so the OLS estimator is inconsistent

5 sources of endogeneity

omitted variables, simultaneous causality, misspessificaton, measurement errors, sample selection

how can you fix simultanous causality

use an instrumental variable regresion

how can you fix misspesification

use a ramsey reset test. if there is evidence of misspessification then we should include non linear terms of the variables and test their significance

exogenous selection of data meaning

unrelated to the variables = ols will be unbiased and consistant

endogenous selection meaning

related to the variables, so need to use a sample selection model

if OVB is present how can we fix this

if we have data on missing variables/know the missing variables, we could include the variable in the regression. if not we may need a diff technique e.g. instrumental variable analysis or panel data

why does simultaneous causlity lead to e being correlated wiht x

if e is negative, y is negative, but if y affects x then when e is negative so is y

how can missing data arise

missing completely, missing based on the value of the dependant, missing based on the value of the explanatory

steps for a ramsey reset test

run the regression without any quadratic/interaction terms. calculate the fitted values of yhati. then calculate y²hati. run a new regression, now adding the new y²hati. test to see if the coefficient of yhat²i is statistically significant. if the coeff is significant, then need to include non-linear terms