1. Introduction - Econometrics at Illinois - University of Illinois at ...

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22 Inference on the Quantile Regression Processas g() and assuming that _g() satises Assumption A.6, then the transformed process~v n () dened by (4.6) can be constructed and similar results to Theorem 3 can beobtained.The above process can be applied to testing the hypothesis that the conditionaldistribution of y i ; conditional on x i , has a continuous cdf F (;), which depends onsome parameters . Thishypothesis can be expressed in the form of (5.4) by settingR =(1; 0; ::::::; 0); r= 1 ,and (; 0 )=F ,1 (; 0 ). In this case, g() corresponds tothe set of linearly independent components of functions (;' 0 ();' 0 ()s() > ). In thecase of the Gaussian hypothesis, the distribution is fully determined by the locationand scale parameters which can be accommodated into R and r by re-standardization,reducing to the hypothesis to the simple formulation (4.4).6. A Reappraisal of the Pennsylvania Reemployment BonusExperimentsA common concern about unemployment insurance (UI) systems has been thesuggestion that the insurance benet acts as a disincentive for job-seekers and thusprolongs the duration of unemployment spells. During the 1980's several controlledexperiments were conducted in the U.S. to test the incentive eects alternative compensationschemes for UI. In these experiments, UI claimants were oered a cashbonus if they found a job within some specied period of time and if the job wasretained for a specied duration. The question addressed by the experiments was:would the promise of such a monetary lump-sum benet provide a signicant inducementfor more intensive job-seeking and thus reduce the duration of unemployment?In the rst experiments conducted in Illinois a random sample of new UI claimantswere told that they would receiveabonus of $500 if they found full-time employmentwithin 11 weeks after ling their initial claim, and if they retained their new job forat least 4 months. These \treatment claimants" were then compared with a controlgroup of claimants who followed the usual rules of the Illinois UI system. The Illinoisexperiment provided very encouraging initial indication of the incentive eects ofsuch policies. They showed that bonus oers resulted in a signicant reduction in theduration of unemployment spells and consequent reduction of the regular amountspaid by the state to UI beneciaries. This nding led to further \bonus experiments"in the states of New Jersey, Pennsylvania and Washington with a variety of newtreatment options. An excellent review of the experiments, some general conclusionsabout their ecacy and a critique of their policy relevance can be found in Meyer(1995), and Meyer (1996). In this section we will focus more narrowly on a reanalysisof data from the Pennsylvania Reemployment Bonus Demonstration described indetail in Corson, Decker, Dunstan, and Keransky (1992).The Pennsylvania experiments were conducted by the U.S. Department ofLaborbetween July 1988 and October 1989. During the enrollment period, claimants whobecame unemployed and registered for unemployment benets in one of the 12 selected
Roger Koenker and Zhijie Xiao 23local oces throughout the state were randomly assigned either to a control groupor one of six experimental treatment groups. In the control group the existing rulesof the unemployment insurance system applied. Individuals in the treatment groupswere oered a cash bonus if they became reemployed in a full-time job, workingmore than 32 hours per week, within a specied qualication period. Two bonuslevels and two qualication periods were tested, but we will restrict attention to thehigh bonus, long qualication period treatment which oered a cash of bonus of sixtimes the weekly benet for claimants establishing reemployment within 12 weeks.This restricted the sample size to 6384 observations. A detailed description of thecharacteristics of claimants under study is presented in Koenker and Bilias (2001)which has information on age, race, gender, number of dependents, location in thestate, existence of recall expectations, and type of occupation.Since a large portion of spells end in either the rst week or the twenty seventhweek, it should be stressed that the denition of the rst spell of UI in the Pennsylvaniastudy includes a waiting week and that the maximum number of uninterruptedfull weekly benets is 26. This implies that many subjects did not receiveanyweeklybenet and that many other claimants received continuously their full, entitled unemploymentbenet. Again, Koenker and Bilias (2001) contains further details.6.1. The Model. Our basic model for analyzing the Pennsylvania experiment presumesthat the logarithm of the duration (in weeks) of subjects' spells of UI benetshave linear conditional quantile functions of the formQ log(T ) (jx) =x > ():The choice of the log transformation is dictated primary by the desire to achievelinearity of the parametric specication and by its ease of interpretation. Multiplicativecovariate eects are widely employed throughout survival analysis, and they arecertainly more plausible in the present application than the assumption of additiveeects. It is perhaps worth reiterating that the role of the transformation is completelytransparent in the quantile regression setting, where Q h(T ) (jx) = x > ()implies Q T (jx) =h ,1 (x > ()). In contrast, the role of transformations in models ofthe conditional mean function are rather complicated since the transformation aectsnot only location, but scale and shape of the conditional distribution of the response.Our (provisional) model includes the following eects: Indicator for the treatment group. Indicators for female, black and hispanic respondents. Number of dependents, with 2 indicating two or more dependents. Indicators for the 5 quarters of entry to the experiment. Indicator for whether the claimant \expected to be recalled" to a previous job. Indicators for whether the respondent was \young" { less than 35, or \old" {indicating age greater than 54. Indicator for whether claimant was employed in the durable goods industry.
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Page 21: and the transformed process isRoger
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