UI STAT 4520 - Bayesian Models for Earnings Dynamics

Unformatted text preview:

IntroductionWhy is this Important?MethodsDataModelConstructingPriorsWinBUGSBayesian Models for Earnings DynamicsGuy Davis Elisa Keller Michael NielsenDepartment of Statistics and Actuarial ScienceThe University of Iowa22S:138 Project PresentationDecember 9, 2009Davis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 1 / 11Introduction Why is this Important?EarningsThe study of earnings inequality across individuals is one of themain fields of economic researchHow does the labor market reward productive attributes likeschooling and work experience?How much of wage inequality is determined by unobservableindividual-specific characteristics?To what extent is inequality spreading over time?Davis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 2 / 11Introduction MethodsOur approachInvestigated the extent to which observable individual-specificcharacteristics shape life-cycle earningsThese characteristics will make up our covariates and include:Years of experience, Gender, and Years of EducationUsed Bayesian regression methods to estimate a standardearning functionAfter checking model diagnostics, investigated fitting subsets offull model to find ’best’ modelDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 3 / 11Introduction DataSimplifying DataThe PSID data set is "a nationally representative longitudinalstudy of nearly 9,000 U.S. families. Following the same familiesand individuals since 1968, the PSID collects data on economic,health, and social behavior."http://psidonline.isr.umich.edu/ and J. Geweke and M. Keane (2000)Narrowed variables from dozens to the ones of interest (Gender,Age, Education, and Wages)Created an ’experience’ variable to replace age; still called "age"(Age - education)Only took a cross section of years(1975,1980,1985,1990,1995,2001)Changed wage over these years to all be in 1975 log(dollars)Davis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 4 / 11Model ConstructingModel’s CoreStarted with a main effects modelHad different coefficients for each yearBeta[1,year[i]] for ith year’s interceptBeta[3,year[i]] for ith year’s gender coefficientetcAdded a random effects term for each individualtheta[subj[i]]Centered variables around their meansNeeded to address correlation due to nature of panel datacar.normal prior on betas was the answerDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 5 / 11Model Priorscar.normalcar.normal also can be used for time-spatial data, not justgeographically spatialadj[] is a vector listing of adjacent time points- accounting for theprior and subsequent yearsweights[] are set to 1 for eachnum[] is a set of time points set to 1 if either 1975 or 2001 and 2otherwiseThis follows the form of a random walk of order 1This modification calls for our initial betas to become (gamma +beta) for each year-betas became a zero mean random error andgamma will be our flat overall mean(gamma[1] + beta[1,year[i]]) + (gamma[2] + beta[2,year[i]]) * (age[i]- age.bar) + ...Thus we created b[1,i]<-gamma[1]+beta[1,i] for each coefficient tomonitorDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 6 / 11Model PriorsPrior Specifics and Initial ValuesSo the car.normal was the prior assigned to beta[] and dflat[] togammaThe beta[]s have a vague precision with their car.normalOne of our models has a precision on intercept betas that areinformative gammas based on our(Elisa’s) prior knowledgeRandom effect for each subject has Normal prior centered at 0with vague precisionRan three chains of initial valuesOne started with estimated values of the b[]s based on a frequentistregression approachOthers were an uninformed, wider range of valuesDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 7 / 11Model WinBUGSModel SelectionWe ran two models: informative and vague precision priors onintercept betaWe monitored DIC but took these results lightly. We based ourmodel selection on the credible intervals of the b[]sRan 2000 iterations, then monitored DIC over 10000 moreiterations.Ran 12000 iterations total (DIC based on last 10000)Burn-in of 2000 iterationsThe two models...Davis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 8 / 11Model WinBUGSVague Intercept Priors 1975 1980 1985 1990 1995 2001 intercept 1.623 1.558 1.555 1.530 1.545 1.648 age 0.013 0.012 0.012 0.010 0.008 0.006 gender -0.459 -0.440 -0.401 -0.341 -0.340 -0.309 educ 0.081 0.075 0.095 0.101 0.115 0.127 DIC 26268.9 Informative Intercept Priors 1975 1980 1985 1990 1995 2001 intercept 1.626 1.556 1.554 1.528 1.541 1.653 age 0.013 0.012 0.012 0.010 0.008 0.006 gender -0.458 -0.439 -0.401 -0.343 -0.340 -0.310 educ 0.081 0.075 0.095 0.101 0.115 0.126 tau.beta1 6.358 6.282 5.922 5.854 5.739 5.648 DIC 26262.2 Davis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 9 / 11Model WinBUGSConclusionsb[]s make sensetau.beta1 decreases over timeDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 10 / 11Model WinBUGSProblems and ComplicationsVery slow interation steps due to complicated model withcar.normalConvergence problems was a recurring theme with most modelsfittedNew concepts - car.normalDavis, Keller, and Nielsen (U of Iowa) Earnings Dynamics 11 /


View Full Document

UI STAT 4520 - Bayesian Models for Earnings Dynamics

Documents in this Course
Load more
Download Bayesian Models for Earnings Dynamics
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Bayesian Models for Earnings Dynamics and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Bayesian Models for Earnings Dynamics 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?