02 Properties of Estimators

02 Properties of Estimators - Economics 140A Properties of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
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.

Page1 / 8

02 Properties of Estimators - Economics 140A Properties of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online