Estimator of a pop. characteristic is consistent if
: has a plim, and its distrib. collapses to a spike as the samp size becomes large and the spike is located at the true value of the pop. characteristic.
)=plimx+plimy+plimz, plim(ax)=aplimx, plimxy=plimxplimy, plim(x/y)=plimx/plimy, plim(f(x))=f(plim(x))
T-Critical > T-Stat: Fail to Reject the Null, T-Stat > T-Critical: Reject the Null
test coefficients on quarterly dum variables are jointly=0.
Q = # of restrictions, n=#of observations, k=dependent variables+intercept,
If F-Crit< F-Stat: reject the null hypothesis.
: w/o any restrictions imposed, contains all variables exactly as in the regression:
: restrictions imposed, regressors whose coefficients have been set to 0 are excluded:
Test of F-Test with R²:
N-K is degrees of freedom,K-1 is #of explanatory variables: Adj Rsquared:
: We assume that the regression is linear in parameters and correctly specified.
We assume that that is no measurement error.
The independent variables are not perfectly correlated and have variation.
independent variables cause the dependent variables and not vice versa.
The expectation of the errors is zero; the second moment is constant, and errors are independent of one another.
We finally assume that the data has a normal
Linear model, regressor values are random from fixed pops, no exact linear relationship exists between regressors, the disturbance term has 0 expectation, homoscedastic, distributed indeoendent of
regressors, zero conditional value, normal distribution and its values have independent distributions.
: means variance not same for all observations, doesn’t affect values on coefficients. We worry because its OLS not BLUE, inefficient estimates, t and f tests are wrong. Know SD? Know it’s a Prob? Use WLS, divide variables by
their variances. If variance is known, divide by S.E.: Yi*=B1Xi1*+B2Xi2*+B3Xi3*+Ui*, the variance of the transformed model is a constant var(ui*)=E(ui/α)²=1/αi²=E(ui)²=1. Variance unknown? There are N variances and K parameters
things to estimate. But, cannot estimate n+k things with only n observations, what to do? Reduce the # of variables to estimate by parameters model.
White vs. GQ?
Use white when you cant assume that the SD of the prob. distr. of the disturbance term is proportional to the size of x, normally distributed, and satisfies other regression assumptions.
: on avg, estimator is correct, the EV of the estimator is the true value
of an estimator is the diff between estimators EV and true value of the parameters estimated; estimator with zero bias is unbiased.