IDEAS home Printed from https://ideas.repec.org/p/fip/feddwp/91593.html

Nonlinear Search and Matching Explained

Author

Abstract

Competing explanations for the sources of nonlinearity in search and matching models indicate that they are not fully understood. This paper derives an analytical solution to a textbook model that highlights the mechanisms that generate nonlinearity and quantifies their contributions. Procyclical variation in the matching elasticity creates nonlinearity in the job finding rate, which interacts with the law of motion for unemployment. These results show the matching function choice is not innocuous. Quantitatively, the Den Haan et al. (2000) matching function more than doubles the skewness of unemployment and welfare cost of business cycles, compared to the Cobb-Douglas specification.

Suggested Citation

  • Joshua Bernstein & Alexander W. Richter & Nathaniel A. Throckmorton, 2021. "Nonlinear Search and Matching Explained," Working Papers 2106, Federal Reserve Bank of Dallas.
    • Handle: RePEc:fip:feddwp:91593
    DOI: 10.24149/wp2106
    as

    Download full text from publisher

    File URL: https://www.dallasfed.org/-/media/documents/research/papers/2021/wp2106.pdf
    File Function: Full text
    Download Restriction: no
    File URL: https://libkey.io/10.24149/wp2106?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Christopher A. Pissarides, 2000. "Equilibrium Unemployment Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161877, December.
    2. Freund, L. B & Rendahl, P., 2020. "Unexpected Effects: Uncertainty, Unemployment, and Inflation," Cambridge Working Papers in Economics 2035, Faculty of Economics, University of Cambridge.
    3. Gary Solon & Ryan Michaels & Michael W. L. Elsby, 2009. "The Ins and Outs of Cyclical Unemployment," American Economic Journal: Macroeconomics, American Economic Association, vol. 1(1), pages 84-110, January.
    4. Jean-Olivier Hairault & Francois Langot & Sophie Osotimehin, 2010. "Matching frictions, unemployment dynamics and the cost of business cycles," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(4), pages 759-779, October.
    5. Lars Ljungqvist & Thomas J. Sargent, 2017. "The Fundamental Surplus," American Economic Review, American Economic Association, vol. 107(9), pages 2630-2665, September.
    6. Melvyn G. Coles & Ali Moghaddasi Kelishomi, 2018. "Do Job Destruction Shocks Matter in the Theory of Unemployment?," American Economic Journal: Macroeconomics, American Economic Association, vol. 10(3), pages 118-136, July.
    7. Merz, Monika, 1995. "Search in the labor market and the real business cycle," Journal of Monetary Economics, Elsevier, vol. 36(2), pages 269-300, November.
    8. Nicolas Petrosky-Nadeau & Lu Zhang & Lars-Alexander Kuehn, 2018. "Endogenous Disasters," American Economic Review, American Economic Association, vol. 108(8), pages 2212-2245, August.
    9. Dupraz, Stéphane & Nakamura, Emi & Steinsson, Jón, 2025. "A plucking model of business cycles," Journal of Monetary Economics, Elsevier, vol. 152(C).
    10. Antoine Lepetit, 2020. "Asymmetric Unemployment Fluctuations and Monetary Policy Trade-Offs," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 36, pages 29-45, April.
    11. Carlo Pizzinelli & Konstantinos Theodoridis & Francesco Zanetti, 2020. "State Dependence In Labor Market Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(3), pages 1027-1072, August.
    12. James D. Hamilton, 2018. "Why You Should Never Use the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 831-843, December.
    13. Alexander Richter & Nathaniel Throckmorton & Todd Walker, 2014. "Accuracy, Speed and Robustness of Policy Function Iteration," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 445-476, December.
    14. Kyle Jurado & Sydney C. Ludvigson & Serena Ng, 2015. "Measuring Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1177-1216, March.
    15. Straub, Ludwig & Ulbricht, Robert, 2015. "Endogenous Uncertainty and Credit Crunches," TSE Working Papers 15-604, Toulouse School of Economics (TSE), revised Dec 2017.
    16. Robert J. Hodrick, 2020. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data," NBER Working Papers 26750, National Bureau of Economic Research, Inc.
    17. Abbritti, Mirko & Fahr, Stephan, 2013. "Downward wage rigidity and business cycle asymmetries," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 871-886.
    18. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    19. Christopher A. Pissarides & Barbara Petrongolo, 2001. "Looking into the Black Box: A Survey of the Matching Function," Journal of Economic Literature, American Economic Association, vol. 39(2), pages 390-431, June.
    20. Barnichon, Regis, 2010. "Building a composite Help-Wanted Index," Economics Letters, Elsevier, vol. 109(3), pages 175-178, December.
    21. Jung, Philip & Kuester, Keith, 2011. "The (un)importance of unemployment fluctuations for the welfare cost of business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1744-1768, October.
    22. Garey Ramey & Wouter J. den Haan & Joel Watson, 2000. "Job Destruction and Propagation of Shocks," American Economic Review, American Economic Association, vol. 90(3), pages 482-498, June.
    23. Robert Shimer, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," American Economic Review, American Economic Association, vol. 95(1), pages 25-49, March.
    24. Dale Mortensen & Eva Nagypal, 2007. "More on Unemployment and Vacancy Fluctuations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(3), pages 327-347, July.
    25. Nicolas Petrosky-Nadeau & Etienne Wasmer, 2017. "Labor, Credit, and Goods Markets," Sciences Po Economics Publications (main) hal-01647732, HAL.
    26. Margaret Stevens, 2007. "New Microfoundations For The Aggregate Matching Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 847-868, August.
    27. Petrosky-Nadeau, Nicolas & Wasmer, Etienne, 2017. "Labor, Credit, and Goods Markets: The Macroeconomics of Search and Unemployment," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262036452, August.
    28. Nigar Hashimzade & Salvador Ortigueira, 2005. "Endogenous Business Cycles With Frictional Labour Markets," Economic Journal, Royal Economic Society, vol. 115(502), pages 161-175, March.
    29. Olivier Blanchard & Jordi Galí, 2010. "Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 1-30, April.
    30. Andolfatto, David, 1996. "Business Cycles and Labor-Market Search," American Economic Review, American Economic Association, vol. 86(1), pages 112-132, March.
    31. Van Nieuwerburgh, Stijn & Veldkamp, Laura, 2006. "Learning asymmetries in real business cycles," Journal of Monetary Economics, Elsevier, vol. 53(4), pages 753-772, May.
    32. Cosmin Ilut & Matthias Kehrig & Martin Schneider, 2018. "Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 2011-2071.
    33. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    34. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
    35. Enrique G. Mendoza, 2010. "Sudden Stops, Financial Crises, and Leverage," American Economic Review, American Economic Association, vol. 100(5), pages 1941-1966, December.
    36. Arthur J. Hosios, 1990. "On The Efficiency of Matching and Related Models of Search and Unemployment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 279-298.
    37. Cristina Arellano & Yan Bai & Patrick J. Kehoe, 2019. "Financial Frictions and Fluctuations in Volatility," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 2049-2103.
    38. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ait Lahcen, Mohammed & Baughman, Garth & Rabinovich, Stanislav & van Buggenum, Hugo, 2022. "Nonlinear unemployment effects of the inflation tax," European Economic Review, Elsevier, vol. 148(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joshua Bernstein & Michael D. Plante & Alexander W. Richter & Nathaniel A. Throckmorton, 2021. "Countercyclical Fluctuations in Uncertainty are Endogenous," Working Papers 2109, Federal Reserve Bank of Dallas.
    2. Joshua Bernstein & Alexander W. Richter & Nathaniel A. Throckmorton, 2025. "The Matching Function and Nonlinear Business Cycles," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 57(2-3), pages 349-376, March.
    3. Bernstein, Joshua & Richter, Alexander W. & Throckmorton, Nathaniel A., 2021. "Cyclical net entry and exit," European Economic Review, Elsevier, vol. 136(C).
    4. Joshua Bernstein & Alexander W. Richter & Nathaniel A. Throckmorton, 2020. "The Business Cycle Mechanics of Search and Matching Models," Working Papers 2026, Federal Reserve Bank of Dallas.
    5. Domenico Ferraro, 2018. "The Asymmetric Cyclical Behavior of the U.S. Labor Market," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 30, pages 145-162, October.
    6. Joshua Bernstein & Alexander W. Richter & Nathaniel A. Throckmorton, 2020. "Entry and Exit, Unemployment, and the Business Cycle," Working Papers 2018, Federal Reserve Bank of Dallas, revised 12 Jan 2021.
    7. Tyler Atkinson & Michael Plante & Alexander Richter & Nathaniel Throckmorton, 2022. "Complementarity and Macroeconomic Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 44, pages 225-243, April.
    8. Matthias S. Hertweck & Vivien Lewis & Stefania Villa, 2021. "Going the Extra Mile: Effort by Workers and Job‐Seekers," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(8), pages 2099-2127, December.
    9. Rendahl, Pontus & Freund, Lukas B., 2020. "Unexpected Effects: Uncertainty, Unemployment, and Inflation," CEPR Discussion Papers 14690, C.E.P.R. Discussion Papers.
    10. Kuo Chun-Hung & Miyamoto Hiroaki, 2019. "Fiscal stimulus and unemployment dynamics," The B.E. Journal of Macroeconomics, De Gruyter, vol. 19(2), pages 1-19, June.
    11. Alexander W. Richter & Nathaniel A. Throckmorton, 2017. "A New Way to Quantify the Effect of Uncertainty," Working Papers 1705, Federal Reserve Bank of Dallas.
    12. Rogerson, Richard & Shimer, Robert, 2011. "Search in Macroeconomic Models of the Labor Market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 7, pages Pages: 61, Elsevier.
    13. Tsasa, Jean-Paul K., 2022. "Labor market volatility in a fully specified RBC search model: An analytical investigation," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    14. Ryuta Ray Kato & Hiroaki Miyamoto, 2013. "Fiscal Stimulus in an Endogenous Job Separation Model," Working Papers EMS_2013_02, Research Institute, International University of Japan.
    15. Dupraz, Stéphane & Nakamura, Emi & Steinsson, Jón, 2025. "A plucking model of business cycles," Journal of Monetary Economics, Elsevier, vol. 152(C).
    16. Joshua Bernstein & Alexander W. Richter & Nathaniel A. Throckmorton, 2020. "COVID-19: A View from the Labor Market," Working Papers 2010, Federal Reserve Bank of Dallas.
    17. Krause, Michael U. & Lopez-Salido, David & Lubik, Thomas A., 2008. "Inflation dynamics with search frictions: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 55(5), pages 892-916, July.
    18. Gomme, Paul & Lkhagvasuren, Damba, 2015. "Worker search effort as an amplification mechanism," Journal of Monetary Economics, Elsevier, vol. 75(C), pages 106-122.
    19. Den Haan, Wouter J. & Freund, Lukas B. & Rendahl, Pontus, 2021. "Volatile hiring: uncertainty in search and matching models," Journal of Monetary Economics, Elsevier, vol. 123(C), pages 1-18.
    20. Miquel Faig, 2008. "Labor Market Cycles and Unemployment Insurance Eligibility," 2008 Meeting Papers 183, Society for Economic Dynamics.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • J63 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Turnover; Vacancies; Layoffs
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:feddwp:91593. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Amy Chapman (email available below). General contact details of provider: https://edirc.repec.org/data/frbdaus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.