- #1
jasper90
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I am sooo lost in this class, please help.
1. Let the true (population) model be y = B0+B1x1+B2x2+u where u is an unobserved error term with u (conditional) x1, x2 and N(0, sigma^2). Hence, u is normally distributed with mean 0 and variance sigma^2 (i.e., E[u (conditional) x1, x2] = 0 and V ar(u (conditional) x1, x2) = sigma^2) conditional on the observed sample. Also, assume that Cov(x1, x2) = sigma(x1x2) does not equal 0.
a) Find y hat = E[y (conditional) x1, x2]
b) Find Var(y (conditional) x1, x2)
c) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + v is the true model and
uses OLS in order to estimate this model. What are the consequences of this in terms of bias and variance
(homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If not why?
d) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + B2x2 + B3x3 + v is the true
model and uses OLS in order to estimate this model. What are the consequences of this in terms of bias and
variance (homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If
not why?Please help.
1. Let the true (population) model be y = B0+B1x1+B2x2+u where u is an unobserved error term with u (conditional) x1, x2 and N(0, sigma^2). Hence, u is normally distributed with mean 0 and variance sigma^2 (i.e., E[u (conditional) x1, x2] = 0 and V ar(u (conditional) x1, x2) = sigma^2) conditional on the observed sample. Also, assume that Cov(x1, x2) = sigma(x1x2) does not equal 0.
a) Find y hat = E[y (conditional) x1, x2]
b) Find Var(y (conditional) x1, x2)
c) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + v is the true model and
uses OLS in order to estimate this model. What are the consequences of this in terms of bias and variance
(homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If not why?
d) Assume that the econometrician (falsely) believes that y = B0 + B1x1 + B2x2 + B3x3 + v is the true
model and uses OLS in order to estimate this model. What are the consequences of this in terms of bias and
variance (homoskedasticity) of parameter estimates. Are the standard errors from this regression valid? If
not why?Please help.