IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2207.10076.html
   My bibliography  Save this paper

Testing for a Threshold in Models with Endogenous Regressors

Author

Listed:
  • Mario P. Rothfelder
  • Otilia Boldea

Abstract

We show by simulation that the test for an unknown threshold in models with endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit severe size distortions both in small and in moderately large samples, pertinent to empirical applications. We propose three new tests that rectify these size distortions. The first test is based on GMM estimators. The other two are based on unconventional 2SLS estimators, that use additional information about the linearity (or lack of linearity) of the first stage. Just like the test in Caner and Hansen (2004), our tests are non-pivotal, and we prove their bootstrap validity. The empirical application revisits the question in Ramey and Zubairy (2018) whether government spending multipliers are larger in recessions, but using tests for an unknown threshold. Consistent with Ramey and Zubairy (2018), we do not find strong evidence that these multipliers are larger in recessions.

Suggested Citation

  • Mario P. Rothfelder & Otilia Boldea, 2022. "Testing for a Threshold in Models with Endogenous Regressors," Papers 2207.10076, arXiv.org.
    • Handle: RePEc:arx:papers:2207.10076
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2207.10076
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Kourtellos, Andros & Stengos, Thanasis & Tan, Chih Ming, 2016. "Structural Threshold Regression," Econometric Theory, Cambridge University Press, vol. 32(4), pages 827-860, August.
    3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    4. Rothfelder, Mario & Boldea, Otilia, 2016. "Testing for a Threshold in Models with Endogenous Regressors," Discussion Paper 2016-029, Tilburg University, Center for Economic Research.
    5. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    6. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    7. Martin Bruns & Michele Piffer, 2021. "Monetary policy shocks over the business cycle: Extending the Smooth Transition framework," University of East Anglia School of Economics Working Paper Series 2021-07, School of Economics, University of East Anglia, Norwich, UK..
    8. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    9. Santoro, Emiliano & Petrella, Ivan & Pfajfar, Damjan & Gaffeo, Edoardo, 2014. "Loss aversion and the asymmetric transmission of monetary policy," Journal of Monetary Economics, Elsevier, vol. 68(C), pages 19-36.
    10. Alpanda, Sami & Granziera, Eleonora & Zubairy, Sarah, 2021. "State dependence of monetary policy across business, credit and interest rate cycles," European Economic Review, Elsevier, vol. 140(C).
    11. Caner, Mehmet & Hansen, Bruce E., 2004. "Instrumental Variable Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 20(5), pages 813-843, October.
    12. Yoon J. Jo & Sarah Zubairy, 2021. "State dependent government spending multipliers: Downward nominal wage rigidity and sources of business cycle fluctuations," Working Papers 20210127-001, Texas A&M University, Department of Economics.
    13. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    14. Antoine, Bertille & Boldea, Otilia, 2018. "Efficient estimation with time-varying information and the New Keynesian Phillips Curve," Journal of Econometrics, Elsevier, vol. 204(2), pages 268-300.
    15. Bertille Antoine & Otilia Boldea, 2015. "Efficient Inference with Time-Varying Information and the New Keynesian Phillips Curve," Discussion Papers dp15-04, Department of Economics, Simon Fraser University, revised 25 Aug 2016.
    16. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    17. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    18. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    19. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    20. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78-121.
    21. Sokbae (Simon) Lee & Hyunmin Park & Myung Hwan Seo & Youngki Shin, 2014. "A contribution to the Reinhart and Rogoff debate: not 90 percent but maybe 30 percent," CeMMAP working papers CWP39/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    22. Michael T. Owyang & Valerie A. Ramey & Sarah Zubairy, 2013. "Are government spending multipliers greater during periods of slack? evidence from 20th century historical data," Working Papers 2013-004, Federal Reserve Bank of St. Louis.
    23. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    24. Robert E. Hall, 2009. "By How Much Does GDP Rise If the Government Buys More Output?," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(2 (Fall)), pages 183-249.
    25. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
    26. Leandro M. Magnusson & Sophocles Mavroeidis, 2014. "Identification Using Stability Restrictions," Econometrica, Econometric Society, vol. 82, pages 1799-1851, September.
    27. 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.
    28. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    29. Valerie A. Ramey & Sarah Zubairy, 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 850-901.
    30. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    31. Lee, Sokbae & Seo, Myung Hwan & Shin, Youngki, 2011. "Testing for Threshold Effects in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 220-231.
    32. Rother, Philipp & Cugnasca, Alessandro, 2015. "Fiscal multipliers during consolidation: evidence from the European Union," Working Paper Series 1863, European Central Bank.
    33. Michael T. Owyang & Valerie A. Ramey & Sarah Zubairy, 2013. "Are Government Spending Multipliers Greater during Periods of Slack? Evidence from Twentieth-Century Historical Data," American Economic Review, American Economic Association, vol. 103(3), pages 129-134, May.
    34. Aart Kraay, 2012. "How large is the Government Spending Multiplier? Evidence from World Bank Lending," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 829-887.
    35. Emi Nakamura & J?n Steinsson, 2014. "Fiscal Stimulus in a Monetary Union: Evidence from US Regions," American Economic Review, American Economic Association, vol. 104(3), pages 753-792, March.
    36. 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.
    37. Valerie Ramey & Sarah Zubairy & Michael Owyang, 2013. "Are Government Spending Multipliers State Dependent? Evidence from U.S. and Canadian Historical Data," 2013 Meeting Papers 290, Society for Economic Dynamics.
    38. Barnichon, Regis & Matthes, Christian, 2018. "Functional Approximation of Impulse Responses," Journal of Monetary Economics, Elsevier, vol. 99(C), pages 41-55.
    39. Ping Yu & Qin Liao & Peter C.B. Phillips, 2019. "Inference and Specification Testing in Threshold Regression with Endogeneity," Cowles Foundation Discussion Papers 2209, Cowles Foundation for Research in Economics, Yale University.
    40. Dimitris Christopoulos & Peter McAdam & Elias Tzavalis, 2021. "Dealing With Endogeneity in Threshold Models Using Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 166-178, January.
    41. Bertille Antoine & Otilia, 2015. "Inference in linear models with structural changes and mixed identification strength," Discussion Papers dp15-05, Department of Economics, Simon Fraser University.
    42. José Luis Montiel Olea & Carolin Pflueger, 2013. "A Robust Test for Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 358-369, July.
    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. Rothfelder, Mario & Boldea, Otilia, 2016. "Testing for a Threshold in Models with Endogenous Regressors," Discussion Paper 2016-029, Tilburg University, Center for Economic Research.
    2. Zacharias Bragoudakis & Dimitrios Panas, 2021. "Investigating government spending multiplier for the US economy: empirical evidence using a triple lasso approach," Working Papers 292, Bank of Greece.

    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. Alogoskoufis, George & Malliaris, A.G. & Stengos, Thanasis, 2023. "The scope and methodology of economic and financial asymmetries," The Journal of Economic Asymmetries, Elsevier, vol. 27(C).
    2. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    3. Marco Bernardini & Selien De Schryder & Gert Peersman, 2020. "Heterogeneous Government Spending Multipliers in the Era Surrounding the Great Recession," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 304-322, May.
    4. Miao, Ke & Li, Kunpeng & Su, Liangjun, 2020. "Panel threshold models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 219(1), pages 137-170.
    5. Valerie A. Ramey, 2019. "Ten Years after the Financial Crisis: What Have We Learned from the Renaissance in Fiscal Research?," Journal of Economic Perspectives, American Economic Association, vol. 33(2), pages 89-114, Spring.
    6. Kim, Hyeongwoo & Zhang, Shuwei, 2018. "Understanding Why Fiscal Stimulus Can Fail through the Lens of the Survey of Professional Forecasters," MPRA Paper 89326, University Library of Munich, Germany.
    7. Kim, Hyeongwoo & Shao, Peng & Zhang, Shuwei, 2023. "Policy coordination and the effectiveness of fiscal stimulus," Journal of Macroeconomics, Elsevier, vol. 75(C).
    8. Miao, Ke & Su, Liangjun & Wang, Wendun, 2020. "Panel threshold regressions with latent group structures," Journal of Econometrics, Elsevier, vol. 214(2), pages 451-481.
    9. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    10. Sebastian Gechert & Ansgar Rannenberg, 2014. "Are Fiscal Multipliers Regime-Dependent? A Meta Regression Analysis," IMK Working Paper 139-2014, IMK at the Hans Boeckler Foundation, Macroeconomic Policy Institute.
    11. Axelle Ferriere & Gaston Navarro, 2013. "The Heterogeneous Effects of Government Spending: It's All About Taxes," Working Papers 13-18, New York University, Leonard N. Stern School of Business, Department of Economics.
    12. Biolsi, Christopher, 2017. "Nonlinear effects of fiscal policy over the business cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 54-87.
    13. Berge, Travis & De Ridder, Maarten & Pfajfar, Damjan, 2021. "When is the fiscal multiplier high? A comparison of four business cycle phases," European Economic Review, Elsevier, vol. 138(C).
    14. El Mostafa Bentour, 2022. "The effects of public debt accumulation and business cycle on government spending multipliers," Applied Economics, Taylor & Francis Journals, vol. 54(19), pages 2231-2256, April.
    15. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205, Edward Elgar Publishing.
    16. Atems, Bebonchu & Yimga, Jules, 2021. "Quantifying the impact of the COVID-19 pandemic on US airline stock prices," Journal of Air Transport Management, Elsevier, vol. 97(C).
    17. Benjamin Born & Gernot J. Müller & Johannes Pfeifer, 2020. "Does Austerity Pay Off?," The Review of Economics and Statistics, MIT Press, vol. 102(2), pages 323-338, May.
    18. Rothfelder, Mario P. & Boldea, Otilia, 2022. "Testing for a Threshold in Models with Endogenous Regressors," Other publications TiSEM 674deead-8826-450a-8f56-f, Tilburg University, School of Economics and Management.
    19. Valerie A. Ramey & Sarah Zubairy, 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 850-901.
    20. Born, Benjamin & D'Ascanio, Francesco & Müller, Gernot & Pfeifer, Johannes, 2019. "Mr. Keynes meets the Classics: Government Spending and the Real Exchange Rate," CEPR Discussion Papers 14073, C.E.P.R. Discussion Papers.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:arx:papers:2207.10076. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.