This preview shows pages 1–3. Sign up to view the full content.
Economics 140A
Properties of Estimators
yields models that describe the evolution of economic variables. The evolution
depends on the value of the parameters that characterize the model. If the pa
rameters are known, and if the distribution of the driving process (or error) is
known, then the evolution is derived using the tools of probability. Because the
parameters of a model are never known, such an approach is infeasible. Instead,
we use the data to infer the parameters; that is, we estimate the parameters.
In studying the evolution of economic variables, we typically focus on one of
three tasks: measurement, testing, or forecasting. If all of the parameters of the
model were known, then measurement of an e/ect would be straightforward (and
equal to a function of the known parameters), testing would be moot (we would
know the parameter value and would not need to conjecture as to whether or not it
unknown future values of the driving process. With unknown parameters replaced
by estimates; measurement is uncertain, testing is important, and forecasting
more ±awed. Clearly the accuracy with which we perform each task depends on
the accuracy of our estimator and so we turn to discussion of how to evaluate
estimators.
An estimator is a function of the data:
Y
=
1
n
P
n
i
=1
Y
i
y
Remark: We distinguish between random variables, which are denoted with
upper case, and the values random variables may take, which are denoted with
lower case. An estimator is a random variable.
Let
A
be an estimator of the parameter
. We study features of the distribution
of
A
. We then turn to a property that is not a feature of the sampling distribution.
The distribution of
A
is obtained by constructing innumerable samples and
plotting the estimate from each sample.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document We begin with the location of the distribution of
A
.
The estimator
A
is unbiased if the expected value of
A
equals
,
EA
=
The bias of
A
measures the departure of
EA
from
,
Bias
(
A
) =
EA
Remark 1: If an estimator is unbiased, the process of drawing repeated sam
ples, obtaining an estimate from each sample, and averaging the estimates will
yield a value that is likely close to the true parameter value. If on average, the
value of the estimator is less than
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 09/04/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.
 Fall '08
 Staff
 Economics

Click to edit the document details