IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/26016.html
   My bibliography  Save this paper

On Testing Continuity and the Detection of Failures

Author

Listed:
  • Matthew Backus
  • Sida Peng

Abstract

Estimation of discontinuities is pervasive in applied economics: from the study of sheepskin effects to prospect theory and “bunching” of reported income on tax returns, models that predict discontinuities in outcomes are uniquely attractive for empirical testing. However, existing empirical methods often rely on assumptions about the number of discontinuities, the type, the location, or the underlying functional form of the model. We develop a nonparametric approach to the study of arbitrary discontinuities — point discontinuities as well as jump discontinuities in the nth derivative, where n = 0,1,... — that does not require such assumptions. Our approach exploits the development of false discovery rate control methods for lasso regression as proposed by G’Sell et al. (2015). This framework affords us the ability to construct valid tests for both the null of continuity as well as the significance of any particular discontinuity without the computation of nonstandard distributions. We illustrate the method with a series of Monte Carlo examples and by replicating prior work detecting and measuring discontinuities, in particular Lee (2008), Card et al. (2008), Reinhart and Rogoff (2010), and Backus et al. (2018b).

Suggested Citation

  • Matthew Backus & Sida Peng, 2019. "On Testing Continuity and the Detection of Failures," NBER Working Papers 26016, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:26016
    Note: IO LS PE TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w26016.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    2. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    3. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    4. Matthew Backus & Thomas Blakee & Brad Larsen & Steven Tadelis, 2020. "Sequential Bargaining in the Field: Evidence from Millions of Online Bargaining Interactions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(3), pages 1319-1361.
    5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    6. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    7. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    8. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    9. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 177-218.
    10. Alexandre Belloni & Victor Chernozhukov & Kengo Kato, 2013. "Uniform post selection inference for LAD regression and other z-estimation problems," CeMMAP working papers CWP74/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Leamer, Edward E, 1983. "Let's Take the Con Out of Econometrics," American Economic Review, American Economic Association, vol. 73(1), pages 31-43, March.
    12. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    13. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    14. Xiaoying Tian & Jonathan Taylor, 2017. "Asymptotics of Selective Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 480-499, June.
    15. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    16. Bruce E. Hansen, 2017. "Regression Kink With an Unknown Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 228-240, April.
    17. Donald, S. G. & Newey, W. K., 1994. "Series Estimation of Semilinear Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 30-40, July.
    Full references (including those not matched with items on IDEAS)

    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. Andrews, Isaiah & Kitagawa, Toru & McCloskey, Adam, 2021. "Inference after estimation of breaks," Journal of Econometrics, Elsevier, vol. 224(1), pages 39-59.
    2. Verme, Paolo & Schuettler, Kirsten, 2021. "The impact of forced displacement on host communities: A review of the empirical literature in economics," Journal of Development Economics, Elsevier, vol. 150(C).
    3. Kurozumi, Eiji & Tuvaandorj, Purevdorj, 2011. "Model selection criteria in multivariate models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 164(2), pages 218-238, October.
    4. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    5. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    6. Adhvaryu, Achyuta & Fenske, James & Khanna, Gaurav & Nyshadham, Anant, 2021. "Resources, conflict, and economic development in Africa," Journal of Development Economics, Elsevier, vol. 149(C).
    7. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    8. Chih‐Hao Chang & Kam‐Fai Wong & Wei‐Yee Lim, 2023. "Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 4-47, February.
    9. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
    10. Davis, Matthew & Ferreira, Fernando, 2022. "Housing disease and public school finances," Economics of Education Review, Elsevier, vol. 88(C).
    11. Jouini, Jamel & Boutahar, Mohamed, 2005. "Evidence on structural changes in U.S. time series," Economic Modelling, Elsevier, vol. 22(3), pages 391-422, May.
    12. Uctum, Merih & Uctum, Remzi, 2011. "Crises, portfolio flows, and foreign direct investment: An application to Turkey," Economic Systems, Elsevier, vol. 35(4), pages 462-480.
    13. Hong, Hui & Chen, Naiwei & O’Brien, Fergal & Ryan, James, 2018. "Stock return predictability and model instability: Evidence from mainland China and Hong Kong," The Quarterly Review of Economics and Finance, Elsevier, vol. 68(C), pages 132-142.
    14. Benati, Luca, 2007. "Drift and breaks in labor productivity," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2847-2877, August.
    15. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    16. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    17. Hervé Le Bihan, 2004. "Tests de ruptures : une application au PIB tendanciel français," Économie et Prévision, Programme National Persée, vol. 163(2), pages 133-154.
    18. van Dijk, D.J.C. & Osborn, D.R. & Sensier, M., 2002. "Changes in variability of the business cycle in the G7 countries," Econometric Institute Research Papers EI 2002-28, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    19. Marianne Sensier & Dick van Dijk, 2004. "Testing for Volatility Changes in U.S. Macroeconomic Time Series," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 833-839, August.
    20. Hui Hong & Zhicun Bian & Chien-Chiang Lee, 2021. "COVID-19 and instability of stock market performance: evidence from the U.S," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-18, December.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:nbr:nberwo:26016. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.