# Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis

## Abstract

**:**

## 1. Introduction

## 2. Labor Market Competition and the Incomplete Data Problem

#### A Maximum Entropy Solution

## 3. Smithian Class of Labor Competition Models

#### 3.1. Quantal Response Statistical Equilibrium

#### 3.1.1. Quantal Response Behavior

#### 3.1.2. Competitive Feedback

#### 3.2. Labor Market Competition with Heterogeneous Workers

## 4. Data

## 5. Labor Competition among Broad Racial and Ethnic Groups in the US

#### Asymmetric Labor Market Competition between Immigrant and Native Workers

## 6. Discussion

#### Limitations and Avenues for Future Research

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Mathematical Appendix

#### Appendix A.1. Analytical Results

#### Appendix A.2. Estimation Approach

## Appendix B. Supplementary Materials

**Table A1.**Summary statistics by sex, ethnic/racial group and census year. Sample size (N), mean and standard deviation (SD) based on the effective sample, below the 98th percentile (P98) cut-off. Dropped categories highlighted.

Year | Sex | Identity | N | Mean | SD | P98 |
---|---|---|---|---|---|---|

1970 | Male | Black Immig. | 429 | 587 | 261 | 1856 |

1970 | Male | Black Native | 56,148 | 549 | 275 | 1856 |

1970 | Male | Hispanic Immig. | 3832 | 607 | 295 | 1856 |

1970 | Male | Hispanic Native | 15,828 | 649 | 305 | 1856 |

1970 | Male | White Immig. | 10,919 | 830 | 342 | 1856 |

1970 | Male | White Native | 517,098 | 804 | 332 | 1856 |

1970 | Female | Black Immig. | 437 | 416 | 231 | 1856 |

1970 | Female | Black Native | 45,135 | 365 | 262 | 1856 |

1970 | Female | Hispanic Immig. | 2113 | 382 | 209 | 1856 |

1970 | Female | Hispanic Native | 6846 | 400 | 239 | 1856 |

1970 | Female | White Immig. | 7341 | 449 | 251 | 1856 |

1970 | Female | White Native | 298,407 | 450 | 266 | 1856 |

1980 | Male | Black Immig. | 5703 | 599 | 315 | 1974 |

1980 | Male | Black Native | 130,068 | 634 | 331 | 1974 |

1980 | Male | Hispanic Immig. | 36,750 | 586 | 317 | 1974 |

1980 | Male | Hispanic Native | 55,001 | 678 | 332 | 1974 |

1980 | Male | White Immig. | 47,538 | 848 | 388 | 1974 |

1980 | Male | White Native | 1,316,415 | 830 | 364 | 1974 |

1980 | Female | Black Immig. | 5720 | 464 | 242 | 1974 |

1980 | Female | Black Native | 132,998 | 454 | 273 | 1974 |

1980 | Female | Hispanic Immig. | 22,587 | 387 | 222 | 1974 |

1980 | Female | Hispanic Native | 36,460 | 421 | 243 | 1974 |

1980 | Female | White Immig. | 40,318 | 452 | 267 | 1974 |

1980 | Female | White Native | 977,997 | 456 | 266 | 1974 |

1990 | Male | Black Immig. | 8761 | 633 | 352 | 2249 |

1990 | Male | Black Native | 121,871 | 640 | 357 | 2249 |

1990 | Male | Hispanic Immig. | 69,225 | 533 | 326 | 2249 |

1990 | Male | Hispanic Native | 68,038 | 680 | 362 | 2249 |

1990 | Male | White Immig. | 44,507 | 890 | 455 | 2249 |

1990 | Male | White Native | 1,478,983 | 821 | 411 | 2249 |

1990 | Female | Black Immig. | 8664 | 547 | 308 | 2249 |

1990 | Female | Black Native | 147,365 | 513 | 313 | 2249 |

1990 | Female | Hispanic Immig. | 42,444 | 403 | 268 | 2249 |

1990 | Female | Hispanic Native | 57,304 | 488 | 294 | 2249 |

1990 | Female | White Immig. | 40,923 | 536 | 340 | 2249 |

1990 | Female | White Native | 1,309,195 | 522 | 325 | 2249 |

2000 | Male | Black Immig. | 13,797 | 677 | 417 | 2800 |

2000 | Male | Black Native | 117,753 | 680 | 402 | 2800 |

2000 | Male | Hispanic Immig. | 100,629 | 531 | 352 | 2800 |

2000 | Male | Hispanic Native | 73,818 | 710 | 411 | 2800 |

2000 | Male | White Immig. | 48,137 | 941 | 567 | 2800 |

2000 | Male | White Native | 1,319,736 | 870 | 484 | 2800 |

2000 | Female | Black Immig. | 14,245 | 585 | 369 | 2800 |

2000 | Female | Black Native | 152,063 | 571 | 362 | 2800 |

2000 | Female | Hispanic Immig. | 60,318 | 415 | 307 | 2800 |

2000 | Female | Hispanic Native | 71,750 | 542 | 349 | 2800 |

2000 | Female | White Immig. | 42043 | 619 | 436 | 2800 |

2000 | Female | White Native | 1,261,430 | 597 | 390 | 2800 |

2010 | Male | Black Immig. | 20,759 | 632 | 417 | 2711 |

2010 | Male | Black Native | 127,333 | 630 | 402 | 2711 |

2010 | Male | Hispanic Immig. | 145,403 | 477 | 327 | 2711 |

2010 | Male | Hispanic Native | 107,518 | 683 | 428 | 2711 |

2010 | Male | White Immig. | 57,760 | 917 | 587 | 2711 |

2010 | Male | White Native | 1,506,568 | 837 | 498 | 2711 |

2010 | Female | Black Immig. | 23,667 | 558 | 380 | 2711 |

2010 | Female | Black Native | 182,544 | 535 | 360 | 2711 |

2010 | Female | Hispanic Immig. | 101,029 | 372 | 287 | 2711 |

2010 | Female | Hispanic Native | 113,748 | 533 | 356 | 2711 |

2010 | Female | White Immig. | 55,435 | 638 | 470 | 2711 |

2010 | Female | White Native | 1,528,697 | 603 | 410 | 2711 |

**Figure A1.**Histogram of observed wage distributions for women, and overlaid fitted marginal (solid) and conditional (dashed) wage distributions. Estimated jointly for all ethnicity groups using the asymmetric Beta QRSE model. 1970–2010 Census and ACS data.

## References

- Bonacich, E. A Theory of Ethnic Antagonism: The Split Labor Market. Am. Sociol. Rev.
**1972**, 37, 547. [Google Scholar] [CrossRef] [PubMed] - Gordon, D.; Edwards, R.; Reich, M. Segmented Work, Divided Workers: The Historical Transformation of Labor in the United States; Cambridge University Press: Cambridge, UK, 1982. [Google Scholar]
- Darity, W.; Hamilton, D.; Stewart, J. A Tour de Force in Understanding Intergroup Inequality: An Introduction to Stratification Economics. Rev. Black Political Econ.
**2015**, 42, 1–6. [Google Scholar] [CrossRef] - Borjas, G.J. The Labor Demand Curve Is Downward Sloping: Reexamining the Impact of Immigration on the Labor Market*. Q. J. Econ.
**2003**, 118, 1335–1374. [Google Scholar] [CrossRef] [Green Version] - Ottaviano, G.I.P.; Peri, G. Rethinking the Effect of Immigration on Wages. J. Eur. Econ. Assoc.
**2012**, 10, 152–197. [Google Scholar] [CrossRef] - Scharfenaker, E.; Foley, D.K. Quantal Response Statistical Equilibrium in Economic Interactions: Theory and Estimation. Entropy
**2017**, 19, 444. [Google Scholar] [CrossRef] - Basso, G.; Peri, G. The Association between Immigration and Labor Market Outcomes in the United States. Technical Report 9436. 2015. Available online: http://ftp.iza.org/dp9436.pdf (accessed on 4 July 2020).
- Foley, D. Social Coordination Problems in Classical and Marxian Political Economy. Rev. Soc. Econ.
**2020**, 78, 4–34. [Google Scholar] [CrossRef] - Scharfenaker, E. Implications of Quantal Response Statistical Equilibrium. J. Econ. Dyn. Control. Available online: https://econ.utah.edu/research/publications/2019-07.pdf (accessed on 4 July 2020).
- Shaikh, A. Capitalism: Competition, Conflict, Crises; Oxford University Press: Oxford, UK, 2016. [Google Scholar]
- Friedman, M. The Methodology of Positive Economics. In Essays in Positive Economics; Univ. of Chicago Press: Chicago, IL, USA, 1953; pp. 3–43. [Google Scholar]
- Smith, A. The Wealth of Nations; Penguin Books: London, UK, 1999. [Google Scholar]
- Foley, D.K. Adam’s Fallacy: A Guide to Economic Theology; Belknap Press of Harvard University Press: Cambridge, MA, USA, 2006. [Google Scholar]
- Jaynes, E.T. Information Theory and Statistical Mechanics. Phys. Rev.
**1957**, 106, 620–630. [Google Scholar] [CrossRef] - Jaynes, E.T. Probability Theory: The Logic of Science; Cambridge University Press: Cambridge, UK, 2003. [Google Scholar]
- Scharfenaker, E.; Semieniuk, G. A Statistical Equilibrium Approach to the Distribution of Profit Rates: Distribution of Profit Rates. Metroeconomica
**2016**, 68, 465–499. [Google Scholar] [CrossRef] - Schneider, M. Evidence for Multiple Labor Market Segments: An Entropic Analysis of US Earned Income, 1996–2007. J. Income Distribution
**2013**, 22, 60–98. [Google Scholar] - Yang, J. A Quantal Response Statistical Equilibrium Model of Induced Technical Change in an Interactive Factor Market: Firm-Level Evidence in the EU Economies. Entropy
**2018**, 20, 156. [Google Scholar] [CrossRef] [Green Version] - Scharfenaker, E.; dos Santos, P.L. The Distribution and Regulation of Tobin’s. Econ. Lett.
**2015**, 137, 191–194. [Google Scholar] [CrossRef] - Scharfenaker, E.; Yang, J. Maximum Entropy Economics. Eur. Phys. J. Spec. Top.
**2020**, 229, 1577–1590. [Google Scholar] [CrossRef] - Cogliano, J.F. Smith’s Perfect Liberty and Marx’s Equalized Rate of Surplus-Value. 2011. Available online: https://pdfs.semanticscholar.org/b80b/97ee9dfa705554f66f3831b9f39a2897935e.pdf (accessed on 4 July 2020).
- Keane, M.P.; Todd, P.E.; Wolpin, K.I. The Structural Estimation of Behavioral Models: Discrete Choice Dynamic Programming Methods and Applications. In Handbook of Labor Economics; Elsevier: Amsterdam, The Netherlands, 2011; Volume 4, pp. 331–461. [Google Scholar]
- Kennan, J.; Walker, J.R. The Effect of Expected Income on Individual Migration Decisions. Econometrica
**2011**, 79, 211–251. [Google Scholar] - Sims, C.A. Implications of Rational Inattention. J. Monet. Econ.
**2003**, 50, 665–690. [Google Scholar] [CrossRef] [Green Version] - Matějka, F.; McKay, A. Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model. Am. Econ. Rev.
**2015**, 105, 272–298. [Google Scholar] [CrossRef] [Green Version] - Wolpert, D.H.; Leslie, D.S. Information Theory and Observational Limitations in Decision Making. B. E. J. Theor. Econ.
**2012**, 12, 1–43. [Google Scholar] [CrossRef] - Wolpert, D.H.; Bono, J.W. Distribution-Valued Solution Concepts. Rev. Behav. Econ.
**2015**, 2, 381–443. [Google Scholar] [CrossRef] - Tilly, C.; Tilly, C. Work Under Capitalism; New Perspectives in Sociology, Westview Press: Boulder, CO, USA, 1998. [Google Scholar]
- Blackwell, K. Entropy Constrained Behavior in Financial Markets A Quantal Response Statistical Equilibrium Approach to Financial Modeling. Ph.D. Thesis, The New School, New York, NY, USA, 2018. [Google Scholar]
- Foley, D.K. A Statistical Equilibrium Theory of Markets. J. Econ. Theory
**1994**, 62, 321–345. [Google Scholar] [CrossRef] - Ruggles, S.; Genadek, K.; Goeken, R.; Grover, J.; Sobek, M. Integrated Public Use Microdata Series: Version 6.0 [Machine-Readable Database]. University of Minnesota, 2015. Available online: https://ipums.org/projects/ipums-usa/d010.v6.0 (accessed on 4 July 2020).
- Portes, A.; Martinez, B.P. They Are Not All the Same: Immigrant Enterprises, Transnationalism, and Development. J. Ethn. Migr. Stud.
**2020**, 46, 1991–2007. [Google Scholar] [CrossRef] - Aldrich, H.E.; Waldinger, R.D. Ethnicity and Entrepreneurship. Annu. Rev. Sociol.
**1990**, 16, 111–135. [Google Scholar] [CrossRef] - Bonacich, E. A Theory of Middleman Minorities. Am. Sociol. Rev.
**1973**, 38, 583. [Google Scholar] [CrossRef] - Cornell, S.; Hartmann, D. Conceptual Confusions and Divides: Race, Ethnicity, and the Study of Immigration. In Not Just Black and White: Historical and Contemporary Perspectives on Immgiration, Race, and Ethnicity in the United States; Foner, N., Fredrickson, G.M., Eds.; Russell Sage Foundation: New York, NY, USA, 2004; pp. 23–41. [Google Scholar]
- Borjas, G.J. Immigration Economics; Harvard University Press: Cambridge, MA, USA, 2014. [Google Scholar]
- Kurre, J.A. Is The Cost Of Living Less In Rural Areas? Int. Reg. Sci. Rev.
**2003**, 26, 86–116. [Google Scholar] [CrossRef] - Massey, D.S.; Denton, N.A. Spatial Assimilation as a Socioeconomic Outcome. Am. Sociol. Rev.
**1985**, 50, 94. [Google Scholar] [CrossRef] - Young, C.; Subbarayan, G. Maximum Entropy Models for Fatigue Damage in Metals with Application to Low-Cycle Fatigue of Aluminum 2024-T351. Entropy
**2019**, 21, 967. [Google Scholar] [CrossRef] [Green Version] - Soofi, E.S.; Ebrahimi, N.; Habibullah, M. Information Distinguishability with Application to Analysis of Failure Data. J. Am. Stat. Assoc.
**1995**, 90, 657–668. [Google Scholar] [CrossRef] - Card, D.; Peri, G. Immigration Economics by George J. Borjas: A Review Essay. J. Econ. Lit.
**2016**, 54, 1333–1349. [Google Scholar] [CrossRef] [Green Version] - Dustmann, C.; Schönberg, U.; Stuhler, J. The Impact of Immigration: Why Do Studies Reach Such Different Results? J. Econ. Perspect.
**2016**, 30, 31–56. [Google Scholar] [CrossRef] [Green Version] - Dickens, W.T.; Lang, K. A Test of Dual Labor Market Theory. Am. Econ. Rev.
**1985**, 75, 792–805. [Google Scholar] - Wang, Q.; Pandit, K. Measuring Ethnic Labour Market Concentration and Segmentation. J. Ethn. Migr. Stud.
**2007**, 33, 1227–1252. [Google Scholar] [CrossRef] - Anderson, B. Migration, Immigration Controls and the Fashioning of Precarious Workers. Work Employ. Soc.
**2010**, 24, 300–317. [Google Scholar] [CrossRef] - Munshi, K. Networks in the Modern Economy: Mexican Migrants in the U. S. Labor Market. Q. J. Econ.
**2003**, 118, 549–599. [Google Scholar] [CrossRef] [Green Version] - Oreopoulos, P. Why Do Skilled Immigrants Struggle in the Labor Market? A Field Experiment with Thirteen Thousand Resumes. Am. Econ. J.
**2011**, 3, 148–171. [Google Scholar] [CrossRef] [Green Version] - Bertrand, M.; Mullainathan, S. Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination. Am. Econ. Rev.
**2004**, 94, 991–1013. [Google Scholar] [CrossRef] [Green Version] - Quillian, L.; Pager, D.; Hexel, O.; Midtbøen, A.H. Meta-Analysis of Field Experiments Shows No Change in Racial Discrimination in Hiring over Time. Proc. Natl. Acad. Sci. USA
**2017**. [Google Scholar] [CrossRef] [Green Version] - Wong, C.; Eccles, J.; Sameroff, A. The Influence of Ethnic Discrimination and Ethnic Identification on African American Adolescents’ School and Socioemotional Adjustment. J. Pers.
**2003**, 71, 1197–1232. [Google Scholar] [CrossRef] - Tomaskovic-Devey, D.; Thomas, M.; Johnson, K. Race and the Accumulation of Human Capital across the Career: A Theoretical Model and Fixed-Effects Application. Am. J. Sociol.
**2005**, 111, 58–89. [Google Scholar] [CrossRef] - dos Santos, P.L.; Wiener, N. By the Content of Their Character? Comparative Group Income Heterogeneity and Socio-Economic Discrimination. J. Math. Sociol.
**2020**, 44, 12–41. [Google Scholar] [CrossRef] - Darity, W.; Dietrich, J.; Guilkey, D.K. Persistent Advantage or Disadvantage?: Evidence in Support of the Intergenerational Drag Hypothesis. Am. J. Econ. Sociol.
**2001**, 60, 435–470. [Google Scholar] [CrossRef] - Stark, O. Rural-to-Urban Migration in LDCs: A Relative Deprivation Approach. Econ. Dev. Cult. Chang.
**1984**, 32, 475–486. [Google Scholar] [CrossRef] - Stark, O.; Taylor, J.E. Migration Incentives, Migration Types: The Role of Relative Deprivation. Econ. J.
**1991**, 101, 1163–1178. [Google Scholar] [CrossRef] - Akerman, A.; Helpman, E.; Itskhoki, O.; Muendler, M.A.; Redding, S. Sources of Wage Inequality. Am. Econ. Rev.
**2013**, 103, 214–219. [Google Scholar] [CrossRef] [Green Version] - Waldinger, R.D.; Lichter, M.I. How the Other Half Works: Immigration and the Social Organization of Labor; University of California Press: Berkeley, CA, USA, 2003. [Google Scholar]
- IWPR. The Gender Wage Gap by Occupation 2016, and by Race and Ethnicity. 2017. Available online: https://iwpr.org/publications/gender-wage-gap-occupation-2016-race-ethnicity/ (accessed on 4 July 2020).
- Folbre, N. Who Pays for the Kids? Gender and the Structures of Constraint; Economics as Social Theory; Routledge: London, UK, 1994. [Google Scholar]
- Economic Policy Institute. Labor Day 2019 | Low-WageWorkers Are Suffering from a Decline in the Real Value of the Federal Minimum Wage. 2019. Available online: https://www.epi.org/publication/labor-day-2019-minimum-wage/ (accessed on 4 July 2020).
- Farber, H.; Herbst, D.; Kuziemko, I.; Naidu, S. Unions and Inequality Over the Twentieth Century: New Evidence from Survey Data; Technical Report w24587; National Bureau of Economic Research: Cambridge, MA, USA, 2018. [Google Scholar]
- Card, D.; Lemieux, T.; Riddell, W.C. Unions and Wage Inequality. J. Labor Res.
**2004**, 25, 519–559. [Google Scholar] [CrossRef] - Dragulescu, A.; Yakovenko, V.M. Statistical Mechanics of Money. Eur. Phys. J. B
**2000**, 17, 723–729. [Google Scholar] [CrossRef] [Green Version] - Drăgulescu, A.; Yakovenko, V.M. Evidence for the Exponential Distribution of Income in the USA. Eur. Phys. J. B
**2001**, 20, 585–589. [Google Scholar] [CrossRef] [Green Version] - Shaikh, A.; Papanikolaou, N.; Wiener, N. Race, Gender and the Econophysics of Income Distribution in the USA. Phys. A
**2014**, 415, 54–60. [Google Scholar] [CrossRef] - Schneider, M. Essays on the Statistical Mechanics of the Labor Market and Implications for the Distribution of Earned Income. Ph.D. Thesis, The New School for Social Research, New York, NY, USA, 2010. [Google Scholar]
- de Brunhoff, S. The State, Capital and Economic Policy; Pluto Press: London, UK, 1978. [Google Scholar]
- Bauder, H. Labor Movement: How Migration Regulates Labor Markets; Oxford University Press: Oxford, UK, 2005. [Google Scholar]
- Cadena, B.C.; Kovak, B.K. Immigrants Equilibrate Local Labor Markets: Evidence from the Great Recession. Am. Econ. J. Appl. Econ.
**2016**, 8, 257–290. [Google Scholar] [CrossRef] [Green Version] - Kapur, J.N.; Kesavan, H.K. Entropy Optimization Principles with Applications; Academic Press: Boston, MA, USA, 1992. [Google Scholar]
- Conceicao, E.L.T. DEoptimR: Differential Evolution Optimization in Pure R. 2016. Available online: https://cran.r-project.org/web/packages/DEoptimR/DEoptimR.pdf (accessed on 4 July 2020).
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2013. [Google Scholar]
- Wickham, H. The Split-Apply-Combine Strategy for Data Analysis. J. Stat. Softw.
**2011**, 40, 1–29. [Google Scholar] [CrossRef] [Green Version] - Wickham, H. Ggplot2: Elegant Graphics for Data Analysis; Springer: New York, NY, USA, 2009. [Google Scholar]

**Figure 1.**Histogram of marginal wage distributions for 2010 ACS data by sex. Overlaid three different specifications of the QRSE model fitted to the data.

**Figure 2.**Soofi’s informational distinguishability/goodness of fit measure for the three QRSE model speficiations, by ethnicity. 1970–2010 Census and ACS data.

**Figure 3.**Histogram of observed wage distributions for men, and overlaid fitted marginal (solid) and conditional (dashed) wage distributions. Estimated jointly for all ethnicity groups using the asymmetric Beta QRSE model. 1970–2010 Census and ACS data.

**Figure 4.**Predicted behavioral responses by race/ethnicity and gender. Selected years, Census and ACS data.

**Figure 5.**Quantal response reference wages (${\mu}_{m}$) and behavioral temperatures (${T}_{m}$) by race/ethnicity and gender. Estimated from the asymmetric QRSE model. 1970–2010 Census and ACS data.

**Figure 6.**Estimated competitive feedback parameters for the impact of exit (${\beta}_{exit}$) and entry (${\beta}_{enter}$) by gender. 1970–2010 Census and ACS data.

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Wiener, N.M.
Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis. *Entropy* **2020**, *22*, 742.
https://doi.org/10.3390/e22070742

**AMA Style**

Wiener NM.
Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis. *Entropy*. 2020; 22(7):742.
https://doi.org/10.3390/e22070742

**Chicago/Turabian Style**

Wiener, Noé M.
2020. "Labor Market Segmentation and Immigrant Competition: A Quantal Response Statistical Equilibrium Analysis" *Entropy* 22, no. 7: 742.
https://doi.org/10.3390/e22070742