錄取率與試題鑑別度對異質考生努力程度及其效用之影響

EFFECTS OF PASS RATE AND TEST DISCRIMINABILITY UPON EFFORTS AND WELFARE OF HETEROGENEOUS EXAM TAKERS

本文在假定學歷僅具傳訊功能的前提下，利用標準的排序競賽模型，從經濟數學模型來探討當考生只有能力為異質時，考試制度的相關變數（如試題鑑別度、錄取率及錄取方式等）將如何影響考生準備考試的努力程度及其效用。根據分析結果，我們發現在不同的能力分布型態與試題鑑別度之下，各種能力考生的努力程度在錄取率提高的過程中會有不同的調整方式，也發現考生在某些狀況下會產生激烈競爭並有其外溢影響。總的來說，本文提出相關的政策思考：「增加偏遠地區教育資源已縮小城鄉差距」及「在差異式錄取率提高下增加試題鑑別度」均有減輕考生負擔及提升整體考生福利的效果。

Under the assumption that a college degree only provides its holders with a high productivity signal for the labor market, this paper adopts a standard tournament model to explore the effects of pass rate, educational expansion arrangement, and test discriminabil-ity upon efforts and welfare of heterogeneous exam takers. Results of numerical analysis suggest that exam takers differ in their responses to an educational expansion when facing various talent distributions and degrees of test discriminability. In some cases, severe competition exists among some group of exam takers, and its effects spill over to other exam takers outside this group. In sum, we propose related policy thinking as follows: increasing either educational resources for disadvantageous students or the degree of test discrim-inability under a differential expansion system can decrease the effort levels in preparing for the exam and raise the total welfare of all exam takers.