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

Roger Koenker and Zhijie Xiao 29for each \slope" coecient. In eect, this approach replaces the matrix standardizationused for the joint test by a scalar standardization. The martingale transformationis then applied just as in the previous case. Now, because there is no matrix standardizationthe original labeling of the coordinates is meaningful. In Table 6.1 wereport the test statistics,K ni =supj~v ni () , ~v ni ( 0 )j= p 1 , 02Tfor each of the covariates. Eects for the 5 quarters of entry are not reported. Thecritical values for these coordinatewise tests are 1.923 at .05, and 2.420 at .01, as givenin Appendix B, so the treatment, race, gender and age eects are highly signicant.Variable Location Scale Shift Location ShiftTreatment 5.41 5.48Female 4.47 4.42Black 5.77 22.00Hispanic 2.74 2.00N-Dependents 2.47 2.83Recall Eect 4.45 16.84Young Eect 3.42 3.90Old Eect 6.81 7.52Durable Eect 3.07 2.83Lusd Eect 3.09 3.05Joint Eect 112.23 449.83Table 6.1. Tests of the Location-Scale-Shift HypothesisAlso reported in Table 6.1 are the corresponding test statistics for the pure locationshifthypothesis. Not surprisingly, we nd that the more restrictive hypothesis ofconstant i () eects is considerably less plausible than the location scale hypothesis.The joint test statistic is now, 449.83, with .01 critical value of 16.00, and all ofthe reported covariates eects are signicant atlevel .05, with the exception of thehispanic eect.7. ConclusionWhat should we conclude from this exercise? The linear location shift and locationscaleshift models are very elegant and convenient abstractions for many statisticalpurposes. However, they also clearly place very stringent restrictions on the way thatcovariates are permitted to inuence the conditional distribution of the response variable.In our unemployment duration application the location-scale shift hypothesismay be viewed as a generalized form of the familiar accelerated failure time model inwhich the scale of the response distribution responds linearly to the covariates. This