Transcription of BAYESIAN ECONOMETRICS - mit.edu
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BAYESIAN ECONOMETRICS - mit.edu
BAYESIAN ECONOMETRICSVICTOR CHERNOZHUKOVB ayesian ECONOMETRICS employs BAYESIAN methods for inference about economicquestions using economic data. In the following, we briefly review these methods andtheir a data vectorX= (X1, .., Xn) follows a distribution with a density func-tionpn(x| ) which is fully characterized by some parameter vector = ( 1, .., d) .Suppose that the prior belief about is characterized by a densityp( ) defined overa parameter space , a subset of a Euclidian spaceRd. Using Bayes rule to incor-porate the information provided by the data, we can form posterior beliefs about theparameter , characterized by the posterior densitypn( |X) =pn(X| )p( )c, c= 1/ pn(X| )p( )d .(1)The posterior densitypn( |X), or simplypn( ), describes how likely it is that aparameter value has generated the observed dataX. We can use the posteriordensity to form optimal point estimates and optimal hypotheses tests.
regions). The posterior fi-quantile µ^ j(fi) for µj (the j-th component of the parameter vector) is the number c such that R £ 1fµj • cgpn(µ)dµ = fi. Properties of Bayesian procedures in both large and small samples are as good as the properties of the procedures based on maximum likelihood.
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