考慮樣本選擇下分析兩性勞工薪資低付問題：關聯結構隨機邊界法之應用

Analyzing Gender Wage Underpayment with Sample Selection: A Copula-based Stochastic Frontier Approach

10.6277/TER.201809_46(3).0003

黃台心(Tai-Hsin Huang)；劉洪禎(Hung-Chen Liu)；胡聚男(Chu-Nan Hu)

樣本選擇 ； 薪資低付 ； 組合誤差項 ； 關聯結構法 ； 隨機邊界關聯結構模型 ； 薪資效率 ； sample selection ； wage underpayment ； composed errors ； copula methods ； stochastic frontier copula model ； wage efficiency

經濟論文叢刊

46卷3期（2018 / 09 / 01）

401 - 450

繁體中文

勞動市場若存在樣本選擇(sample selection)問題，本研究嘗試建構聯立迴歸模型，同時包含隨機工資與工時兩條邊界方程式，可探討男女兩性勞工薪資低付程度課題。因存在組合誤差項，必須使用關聯結構法推導出聯合機率密度函數，進而建構隨機邊界關聯結構模型。整理民國94、96、98、100與102等五年的台灣「人力運用調查」資料，進行迴歸分析。發現考慮樣本選擇的平均薪資效率遠低於未考慮樣本選擇者，與以往文獻有相當差異，可能原因為以往文獻探討薪資效率時，未同時考慮樣本選擇問題，將無工作者樣本完全排除，導致迴歸分析結果僅適用於有工作者。

This paper compiles the ＂Manpower Utilization Survey＂ data, to study the issue of wage underpayment. Assuming sample selection, we apply copula methods to derive the joint probability density function for composed errors in the equations of wage and hours of work. The likelihood function can take both workers, who have observed wages, and non-workers, who have no observed wages, into account. Non-workers are usually excluded by previous researchers, studying similar issues, since they overlook the role of sample selection. The empirical results show that the trend of wage efficiency in the categories of working identity and working area are almost the same in each gender, whether correcting for the sample selection problem or not. However, in the remaining 4 categories, the sample selection bias appears to play an important role on the determination of wage efficiency. With the correction of the samples election bias, most of the findings differ from the past literature that considers only workers with wages and salary.

1. 徐美、陳明郎、方俊德(2006)。台灣產業結構變遷和性別歧視對男女薪資溢酬變動趨勢之影響。經濟論文，34，505-539。
   連結：
2. 陳建良、管中閔(2006)。台灣工資函數與工資性別歧視的分量迴歸分析。經濟論文，34，435-468。
   連結：
3. Adamchik, Vera A.,King, Arthur E.(2007).Labor Market Efficiency in Poland: A StochasticWage Frontier Analysis.International Journal of Business and Finance Research,1,41-50.
4. Aigner, Dennis,Lovell, Charles Albert Knox,Schmidt, Peter(1977).Formulation and Estimation of Stochastic Frontier Production Function Models.Journal of Econometrics,6,21-37.
5. Battese, George E.,Coelli, Tim J.(1988).Prediction of Firm-Level Technical Efficiencies with a Generalized Frontier Production Function and Panel Data.Journal of Econometrics,38,387-399.
6. Bishop, John A.,Grodner, Andrew,Liu, Haiyong,Chiou, Jong-Rong(2007).Gender Earnings Differentials in Taiwan: A Stochastic Frontier Approach.Journal of Asian Economics,18,934-945.
7. Brown, Sarah,Roberts, Jennifer,Taylor, Karl(2011).The Gender Reservation Wage Gap: Evidence from British Panel Data.Economics Letters,113,88-91.
8. Carter, Hill, R.,Griffiths, William E.,Lim, Guay C.(2012).Principles of Econometrics, International Student Version.New Jersey:John Wiley and Sons.
9. Cotton, Jeremiah(1988).On the Decomposition of Wage Differentials.Review of Economics and Statistics,70,236-243.
10. Díaz, M. Ángeles,Sánchez, Rosario(2013).Young Workers, Marital Status and Wage Gap.Revista de economía aplicada,21,57-70.
11. Díaz, M. Ángeles,Sánchez, Rosario(2011).Gender and Potential Wage in Europe: A Stochastic Frontier Approach.International Journal of Manpower,32,410-425.
12. Gannicott, Kenneth(1986).Women, Wages, and Discrimination: Some Evidence from Taiwan.Economic Development and Cultural Change,34,721-730.
13. Gørgens, Tue(2002).Reservation Wages and Working Hours for Recently Unemployed US Women.Labour Economics,9,93-123.
14. Heckman, James J.(1974).Shadow Prices, MarketWages, and Labor Supply.Econometrica,42,679-694.
15. Heckman, James J.(1976).The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for SuchModels.Annals of Economic and Social Measurement,5,475-492.
16. Hofler, Richard A.,Murphy, Kevin J.(1994).Estimating Reservation Wages of EmployedWorkers Using a Stochastic Frontier.Southern Economic Journal,961-976.
17. Hofler, Richard A.,Murphy, Kevin J.(1992).Underpaid and Overworked: Measuring the Effect of Imperfect Information on Wages.Economic Inquiry,30,511-529.
18. Hofler, Richard A.,Polachek, SolomonW.(1985).A New Approach for Measuring Wage Ignorance in the Labor Market.Journal of Economics and Business,37,267-276.
19. Jondrow, James,Lovell, Charles Albert Knox,Materov, Ivan S.,Schmidt, Peter(1982).On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Function Model.Journal of Econometrics,19,233-238.
20. Lai, Hung-Pin,Huang, Cliff J.(2013).Maximum Likelihood Estimation of Seemingly Unrelated Stochastic Frontier Regressions.Journal of Productivity Analysis,40,1-14.
21. Lang, Günter(2005).The Difference between Wages and Wage Potentials: Earnings Disadvantages of Immigrants in Germany.Journal of Economic Inequality,3,21-42.
22. Mincer, Jacob(1974).Schooling, Experience, and Earnings.New York:Columbia University Press.
23. Oaxaca, Ronald(1973).Male-Female Wage Differentials in Urban Labor Markets.International Economic Review,14,693-709.
24. Ogloblin, Constantin,Brock, Gregory(2005).Wage Determination in Urban Russia: Underpayment and the Gender Differential.Economic Systems,29,325-343.
25. Pannenberg, Markus(2010).Risk Attitudes and Reservation Wages of Unemployed Workers: Evidence from Panel Data.Economics Letters,106,223-226.
26. Polachek, Solomon W.,Xiang, Jun Jeff(2006).The Effects of Incomplete EmployeeWage Information: A Cross-Country Analysis.Research in Labor Economics,24,35-75.
27. Polachek, Solomon W.,Yoon, Bong Joon(1987).A Two-Tiered Earnings Frontier Estimation of Employer and Employee Information in the Labor Market.Review of Economics and Statistics,296-302.
28. Robinson, Michael D.,Wunnava, Phanindra V.(1989).Measuring Direct Discrimination in Labor Markets Using a Frontier Approach: Evidence from CPS Female Earnings Data.Southern Economic Journal,1,212-218.
29. Sklar, Abe(1959).Fonctions de Répartition à n Dimensions et Leurs Marges.Publications de l'Institut de Statistique de l'Université de Paris,8,229-231.
30. Tsay,Wen-Jen,Huang, Cliff J.,Fu, Tsu-Tan,Ho, I-Lin(2013).A Simple Closed-Form Approximation for the Cumulative Distribution Function of the Composite Error of Stochastic Frontier Models.Journal of Productivity Analysis,39,259-269.
31. Wang, Hung-Jen(2002).Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model.Journal of Productivity Analysis,18,241-253.
32. Webb, Robert,Watson, Duncan,Hinks, Tim(2003).Testing for Wage Over-Payment in UK Financial Services: A Stochastic Frontier Approach.Service Industries Journal,23,123-136.
33. 王素彎、連文榮(1989)。台灣地區勞動市場的性別歧視。台灣銀行季刊，40，363-381。
34. 江錦淑(2008)。國立中正大學國際經濟研究所=Graduate Institute of International Economics, National Chung Cheng University。
35. 林忠正(1988)。初入勞動市場階段之工資性別差異。經濟論文叢刊，16，205-322。
36. 邱曉培(1997)。台灣地區工資的性別差異。勞工研究，128，43-85。
37. 高長(1990)。職業選擇與性別工資差異：台灣地區之實證分析。人口變遷與經濟社會發展研討會，台北=Taipei:
38. 曾敏傑(2001)。台灣地區兩性薪資差異與變遷：1982、1992及2000年的比較。人口學刊，23，147-209。
39. 黃台心、熊一鳴(1992)。台灣地區男女全職與兼職工作工資差異之研究。台灣銀行季刊，43，327-347。
40. 劉佳苓(1997)。台灣地區之職業性別隔離。勞工研究，130，75-94。
41. 劉錦添、詹方冠(1990)。隨機性工資邊界函數與工資報酬的性別歧視。人口變遷與經濟社會發展研討會，台北=Taipei:
42. 劉錦添、劉錦龍(1987)。台灣地區男女工資率的差異。中國經濟學會年會論文集
43. 劉鶯釧(1989)。台灣地區受雇人員工資的性別歧視。經濟論文叢刊，17，359-388。
44. 薛立敏(1988)。就業市場性別歧視的經濟分析。經濟前瞻，10，131-132。