lecture 12

Question 1

is it always optimal to chose an unbiased estimator over a biased estimator

Answer 1

It is not always optimal to choose an unbiased estimator over a
biased estimator if the variance of the unbiased estimator is much
higher.

Question 2

what is an alternative criteria to chose an estimator

Answer 2

An alternative criterion is to choose the estimator with the lowest
mean square error.
=𝑉(𝛽̂ )+”bia” “s” ^2

Question 3

how do you test for functional form

Answer 3

linear functional form is not appropriate then higher powers of
the explanatory variables should be included in the regression.

but if we include all these variables in our regression then there
is a danger of multicollinearity.

Instead include the squared fitted values from a linear regression
and test if these are significant.

basically all the square values will = Yhat squared

Question 4

what is the test for functional form misspecification

Answer 4

This is the Ramsey reset test for functional form misspecification.

This test can be generalised by adding cubic and higher order
powers of the fitted values series.

Question 5

what is serial correlation?

Answer 5

Serial correlation is a problem associated with time-series
data.

It occurs when the errors of the regression model are
correlated with their own past values.

Serial correlation by itself does not mean that OLS will
be biased.

The most common effect of serial correlation is to bias
downwards the standard errors of the OLS estimator
(though this is not always the case).

Question 6

definition of serial correlated

Answer 6

errors from 2016 can be correlated with errors with 2017

𝐸(𝑢_𝑡 𝑢_(𝑡−𝑘) )≠0”for “

Question 7

what is autocorrelation?

Answer 7

Autocorrelation is a particular type of serial correlation in which
the error terms are a function of their own past values.

Question 8

what is the orders of serial correlation

Answer 8

In general the order of serial correlation refers to the maximum
lag on the right hand side of the equation describing the error
term.

The order of the serial correlation process is often related to the
frequency of the data. For example, models estimated with
quarterly data often have errors which exhibit fourth-order
autocorrelation.

Question 9

how do you detect serial correlation

Answer 9

set up a correlogram

look at it, you can see the type of correlation like that