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Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function

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  • Daniel Gutknecht

Abstract

This paper develops a test for monotonicity of nonparametric regression models under endogeneity, which in its generality is novel in the literature.� The test statistic, which is built upon a second order U-process, introduces 'correction terms' based on control functions that purge the endogeneity.� The test has a non-standard asymptotic distribution from which asymptotic critical values can directly be derived.� Furthermore, the test statistic is extended to accommodate multivariate (exogenous) regressors.� Consistency against general alternatives is proved and the test's finite sample properties are examined in a Monte Carlo experiment.� The test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration.� This relationship is difficult to measure due to the simultaneity of both variables.� Preliminary results indicate that reservation wage functions do in fact not decline monotonically.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 673.

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Date of creation: 18 Sep 2013
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Handle: RePEc:oxf:wpaper:673

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Keywords: control function; endogeneity; reservation wages; test for monotonicity;

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  1. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2006. "Testing for stochastic monotonicity," LSE Research Online Documents on Economics 4425, London School of Economics and Political Science, LSE Library.
  2. Kiefer, Nicholas M & Neumann, George R, 1979. "An Empirical Job-Search Model, with a Test of the Constant Reservation-Wage Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 89-107, February.
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  7. Richard Blundell & Rosa Matzkin, 2010. "Conditions for the existence of control functions in nonseparable simultaneous equations models," CeMMAP working papers CWP28/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
  9. Addison, John T. & Centeno, Mario & Portugal, Pedro, 2004. "Reservation Wages, Search Duration, and Accepted Wages in Europe," IZA Discussion Papers 1252, Institute for the Study of Labor (IZA).
  10. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  11. Smith, Jennifer, 2010. "The Ins and Outs of UK Unemployment," The Warwick Economics Research Paper Series (TWERPS) 944, University of Warwick, Department of Economics.
  12. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  13. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
  14. van den Berg, Gerard J, 1990. "Nonstationarity in Job Search Theory," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 255-77, April.
  15. Sarah Brown & Karl Taylor, . "Reservation Wages, Expected wages and the duration of Unemployment: evidence from British Panel data," Working Papers 2009001, The University of Sheffield, Department of Economics.
  16. Garen, John, 1984. "The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable," Econometrica, Econometric Society, vol. 52(5), pages 1199-1218, September.
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