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Smooth transition trends and labor force participation rates in the United States

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Abstract

This paper employs smooth transition trend models to investigate the long-run time series behavior of quarterly US labor force participation rates. In particular, we examine whether long-run growth in labor force participation rates can be modeled by smooth transitions between states rather than as abrupt mean level changes or as a stochastic trend. Smooth transitions permit for non-instantaneous adjustment of individual workers to changes associated with economic events or general labor market conditions. We employ unit root testing procedures with alternatives characterized by stationary fluctuations around one or two smooth transitions in linear trend. We examine labor force participation rates by gender- and age-specific groups. The results indicate that all female and most male participation series are better characterized as stationary processes that undergo transitional deterministics.

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Notes

  1. Most of these studies question on the informational value of unemployment rates or the presence of unemployment hysteresis (see the relevant study of Gustavsson and Österholm 2010), with evidence of non-stationary participation rates implying hysteresis in unemployment and uncertainty about the relation between long-term changes in unemployment and employment rates (see Madsen et al. 2008 for further discussion).

  2. Upon estimation, time \(t\) in the transition function is scaled between 0 and 1 replacing \(t\) with \(t/T\) and \(t-\tau T\) with \(t/T-\tau .\)

  3. Our sample consists of 253 quarterly observations on labor force participation rates.

  4. We have also computed the (Phillips and Perron (1988), PP) and the Ng and Perron (2001) \(MZ_{a}^{GLS}\) unit root tests. The results from these tests are not reported (they are available upon request), yet they are in full agreement with the ADF and the DF-GLS test results reported in the paper (with respect to non-stationarity decision). All unit root tests have been carried out in EViews 7.2

  5. For brevity, these results are not reported. They are available upon request.

  6. All results reported from the smooth transition unit root tests were obtained using programs written by the authors in Ox version 5.10, see Doornik (2007).

  7. Participation rate of men 20–24 dropped rapidly after the 2007 recession (Fig. 2c), and this decrease affected the NLS estimation and the calculation of the non-linear ADF statistic. In order to continue testing for structural changes in this participation rate, we decide to cut the last seven observations.

  8. Perron (2006), Sect. 8.5, reviews and discusses unit root versus trend stationarity in the presence of structural change in the trend function.

References

  • Bacon DW, Watts DG (1971) Estimating the transition between two intersecting straight lines. Biomertika 58:525–534

    Article  Google Scholar 

  • Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78

    Article  Google Scholar 

  • Benati L (2001) Some empirical evidence on the ‘discouraged worker’ effect. Econ Lett 70:387–395

    Article  Google Scholar 

  • Caner M, Hansen BE (2001) Threshold autoregression with a unit root. Econometrica 69(6):1555–1596

    Article  Google Scholar 

  • Dagsvik JK, Kornstad T, Skjerpen T (2012) Labor force participation and the discouraged worker effect. Empir Econ. doi:10.1007/s00181-012-0598-9

  • Darby J, Hart RA, Vecchi M (2001) Labour force participation and the business cycle: a comparative analysis of France, Japan, Sweden and the United States. Jpn World Econ 13:113–133

    Article  Google Scholar 

  • DiCecio R, Engemann MK, Owyang TM, Wheeler HC (2008) Changing trends in the labor force: a survey. Fed Reserve Bank of St. Louis Rev 90(1):47–62

    Google Scholar 

  • Dickey DA, Fuller W (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74(366):427–431

    Google Scholar 

  • Doornik JA (2007) Object-oriented matrix programming using ox, 3rd edn. Timberlake Consultants Press and Oxford, London. www.doornik.com.

  • Elliott G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64:813–836

    Article  Google Scholar 

  • Gil-Alana LA (2008) Fractional integration and structural breaks at unknown periods of time. J Time Ser Anal 29(1):163–185

    Article  Google Scholar 

  • Granger CWJ, Teräsvirta T (1993) Modelling nonlinear economic relationships. Oxford University Press, Oxford

    Google Scholar 

  • Greenway D, Leybourne SJ, Sapsford D (1997) Modelling growth and liberalisation using smooth transition analysis. Econ Inq 35:798–814

    Article  Google Scholar 

  • Greenway D, Leybourne SJ, Sapsford D (2000) Smooth transitions and GDP growth in the European union. Manch Sch 68(2):145–165

    Article  Google Scholar 

  • Greenwood J, Seshardi A, Yorukoglou M (2005) Engines of liberation. Rev Econ Stud 72(1):109–133

    Article  Google Scholar 

  • Gustavsson M, Österholm P (2006) The informational value of unemployment statistics: a note on the time series properties of participation rates. Econ Lett 92(3):428–433

    Article  Google Scholar 

  • Gustavsson M, Österholm P (2010) The presence of unemployment hysteresis in the OECD: what can we learn from out-of-sample forecasts? Empir Econ 38:779–792

    Article  Google Scholar 

  • Gustavsson M, Österholm P (2012) Labor-force participation rates and the informational value of unemployment rates: evidence from disaggregated US data. Econ Lett 116:408–410

    Article  Google Scholar 

  • Haldrup N (1998) An econometric analysis of I(2) variables. J Econ Surv 12(5):595–650

    Article  Google Scholar 

  • Harvey DI, Mills TC (2002) Unit roots and double smooth transitions. J Appl Stat 29:675–683

    Article  Google Scholar 

  • Hotchkiss JL, Robertson JC (2012) Asymmetric labour force participation decisions. Appl Econ 44(16):2065–2073

    Google Scholar 

  • Im KS, Pesaran MH, Shin Y (2003) Testing for unit roots in heterogeneous panels. J Econom 115(1):53–74

    Article  Google Scholar 

  • Jacobsen JP (1999) Labor force participation. Q Rev Econ Financ 39:597–610

    Google Scholar 

  • Johansen S (1988) Statistical analysis of cointegration vectors. J Econ Dyn Control 12:231–254

    Article  Google Scholar 

  • Juhn C (1992) Decline of male labor force participation: the role of declining market opportunities. Q J Econ 107(1):79–121

    Google Scholar 

  • Juhn C, Potter S (2006) Changes in labor force participation in the United States. J Econ Perspect 20(3): 27–46

    Article  Google Scholar 

  • Kapetanios G, Shin Y, Snell A (2003) Testing for a unit root in the nonlinear STAR framework. J Econom 112:359–379

    Google Scholar 

  • Killingsworth RM, Heckman JJ (1986) Female labor supply: a survey. In: Ashenfelter O, Layard R (eds) Handbook of labor economics, vol 1. Harvard University Press, Cambridge, pp 103–204

    Google Scholar 

  • Kwiatkowski D, Phillips PCB, Schmidt P, Yongcheol S (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. J Econom 54:159–178

    Google Scholar 

  • Landajo M, Presno MJ (2010) Nonparametric pseudo-Lagrange multiplier stationarity testing. MPRA Paper No. 25659, http://mpra.ub.uni-muenchen.de/25659/

  • Lee J, Strazicich MC (2003) Minimum lagrange multiplier unit root test with two structural breaks. Rev Econ Stat 85(4):1082–1089

    Article  Google Scholar 

  • Lee J, Strazicich MC (2004) Minimum LM unit root test with one structural break. Working paper No 04–17 Department of Economics, Appalachian State University.

  • Leybourne SJ, Mizen P (1999) Understanding the disinflations in Australia, Canada and New Zealand using evidence from smooth transition analysis. J Int Money Finance 18:799–816

    Article  Google Scholar 

  • Leybourne SJ, Newbold P, Vougas D (1998) Unit roots and smooth transition analysis. J Time Ser Anal 19(1):83–97

    Article  Google Scholar 

  • Lin CJ, Teräsvirta T (1994) Testing the constancy of regression parameters against continuous structural change. J Econom 62:211–228

    Google Scholar 

  • Madsen J, Mishra V, Smyth R (2008) Are labour force participation rates non-stationary? Evidence from 130 years for G7 countries. Aust Econ Pap June, 66–189.

  • McEwen H, Orrenius R, Wynne M (2005) Opting out of work: what’s behind the decline in labor force participation?. Fed Reserve Bank of Dallas, Issue 6

  • Michael RT (1985) Consequences of the rise in female labor force participation rates: questions and robes. Part 2: trends in women’s work, education, and family, building. J Labor Econ 3(1):S117–S146

    Article  Google Scholar 

  • Murphy KM, Topel R (1997) Unemployment and nonemployment. Am Econ Rev 87(2):295–300

    Google Scholar 

  • Ng S, Perron P (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554

    Article  Google Scholar 

  • Ozdemir ZA, Balcilar M, Tansel A (2012) International labour force participation rates by gender: unit root or structural breaks? Bull Econ Res. doi:10.1111/j.1467-8586.2011.00419.x

  • Pencavel H (1986) Labor supply of men: a survey. Chap. 1. In: Ashenfelter O, Layard R (eds) Handbook of labor economics, vol 1. Elsevier, North-Holland, pp 3–102

    Google Scholar 

  • Peracchi F, Welch F (1994) Trends in labor force transitions of older men and women. J Labor Econ 12(2):210–242

    Article  Google Scholar 

  • Perron P (2006) Dealing with Structural Breaks. In: Patterson K, Mills TC (eds) Palgrave Handbook of Econometrics, Econometric Theory, vol 1. Palgrave Macmillan, Basingstoke, pp 278–352

    Google Scholar 

  • Perron P, Qu Z (2007) A simple modification to improve the finite sample properties of Ng and Perron’s unit root tests. Econ Lett 94:12–19

    Article  Google Scholar 

  • Phillips PCB, Perron P (1988) Testing for unit roots in time series regression. Biometrika 75:423–470

    Article  Google Scholar 

  • Robinson PM (1994) Efficient tests of nonstationary hypotheses. J Am Stat Assoc 89:1420–1437

    Article  Google Scholar 

  • Said SE, Dickey DA (1984) Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71:599–607

    Article  Google Scholar 

  • Smith PJ, Ward M (1985) Time series changes in the female labor force. J Labor Econ 3(2):59–90

    Article  Google Scholar 

  • Sollis R (2005) Evidence on purchasing power parity from univariate models: the case of smooth transition trend-stationarity. J Appl Econom 20:79–98

    Google Scholar 

  • Sollis R, Leybourne SJ, Newbold P (1999) Unit roots and asymmetric smooth transitions. J Time Ser Anal 20(6):671–677

    Article  Google Scholar 

  • Van Zandweghe W (2012) Interpreting the recent decline in labor force participation. Fed Reserve Bank of Kansas City, Econ Rev, First Quarter, 5–34

  • Vougas DV (2006) On unit root testing with smooth transitions. Comput Stat Data Anal 51: 797–800

    Google Scholar 

  • White H (1980) A heteroskedasticity-consistent covariance matrix and a direct test for heteroskedasticity. Econometrica 48:817–838

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank an anonymous Associate Editor and two anonymous referees for their valuable comments and suggestions on this paper. Authors bare sole responsibility for any errors that may remain.

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  1. Department of Economics, University of Patras, University Campus, 26504 , Rio, Greece

    Paraskevi K. Salamaliki & Ioannis A. Venetis

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  1. Paraskevi K. Salamaliki
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Correspondence to Ioannis A. Venetis.

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Salamaliki, P.K., Venetis, I.A. Smooth transition trends and labor force participation rates in the United States. Empir Econ 46, 629–652 (2014). https://doi.org/10.1007/s00181-013-0690-9

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