{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Econometrics-I-24

Bbar_1.21483281.05076663

Info iconThis preview shows pages 17–24. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: +---------+--------------+----------------+--------+---------+BBAR_1 .21483281 .05076663 4.232 .0000BBAR_2 .40815611 .04779292 8.540 .0000BBAR_3 -.49692480 .04508507 -11.022 .0000+---------+--------------+----------------+--------+---------+|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |+---------+--------------+----------------+--------+---------+B_1 .22696546 .04276520 5.307 .0000B_2 .40038880 .04671773 8.570 .0000B_3 -.50012787 .04705345 -10.629 .0000˜˜™™™ 16/34Part 24: Bayesian EstimationA Random Effects ApproachpAllenby and Rossi, “Marketing Models of Consumer Heterogeneity”nDiscrete Choice Model – Brand Choicen“Hierarchical Bayes”nMultinomial ProbitpPanel Data: Purchases of 4 brands of Ketchup˜˜™™™ 17/34Part 24: Bayesian EstimationStructure˜˜˜™™™ 18/34,,,,,,Conditional data generation mechanism*, .1[*](constant, log price, "availability," "fit jiit jit jit jit jit jyUtility for consumer i, choice t, brand jYymaximum utility among the J choicesε=+===xxβ,1eatured")~[0,],Implies a J outcome multinomial probit model.it jjNελλ =Part 24: Bayesian EstimationBayesian Priors˜˜˜™™™ 19/341~[ ,], ,~[ ,]~[ ,] (looks like chi-squared), =3, 1~[ ,], ~[ ,],8,iiiijjiPrior DensitiesNImpliesNInverse Gamma v svsPriors over model parametersNaWishart vv-=+===Vw wVVVVVββββλβββββββ8=IPart 24: Bayesian EstimationBayesian EstimatorpJoint Posterior=pIntegral does not exist in closed form.pEstimate by random samples from the joint posterior.pFull joint posterior is not known, so not possible to sample from the joint posterior.˜˜˜™™™ 20/3411[,...,,,,,...,|]NJEVdataββββλλPart 24: Bayesian EstimationGibbs Cycles for the MNP ModelpSamples from the marginal posteriors˜˜˜™™ 21/34Marginal posterior for the individual parameters(Known and can be sampled)| ,, ,Marginal posterior for the common parameters (Each known and each can be sampled)|, ,| , ,idatadatadaβββVVVββλβλβ λ|,,tadataβVλ β,Part 24: Bayesian EstimationResultspIndividual parameter vectors and disturbance variancespIndividual estimates of choice probabilitiespThe same as the “random parameters model” with slightly different weights.pAllenby and Rossi call the classical method an “approximate Bayesian” approach.n(Greene calls the Bayesian estimator an “approximate random parameters model”)nWho’s right?pBayesian layers on implausible uninformative priors and calls the maximum likelihood results “exact” Bayesian estimatorspClassical is strongly parametric and a slave to the distributional assumptions.pBayesian is even more strongly parametric than classical....
View Full Document

{[ snackBarMessage ]}

Page17 / 35

BBAR_1.21483281.05076663 4.232.0000BBAR_2.40815611.04779292...

This preview shows document pages 17 - 24. Sign up to view the full document.

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