IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2505.22388.html
   My bibliography  Save this paper

A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data

Author

Listed:
  • Zhentao Shi
  • Jin Xi
  • Haitian Xie

Abstract

This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating counterfactual outcomes, we caution researchers against assuming a common nonstationary trend factor across units for macroeconomic outcomes, as doing so may result in misleading causal estimation-a pitfall we refer to as the spurious synthetic control problem. To address this issue, we propose a synthetic business cycle framework that explicitly separates trend and cyclical components. By leveraging the treated unit's historical data to forecast its trend and using control units only for cyclical fluctuations, our divide-and-conquer strategy eliminates spurious correlations and improves the robustness of counterfactual prediction in macroeconomic applications. As empirical illustrations, we examine the cases of German reunification and the handover of Hong Kong, demonstrating the advantages of the proposed approach.

Suggested Citation

  • Zhentao Shi & Jin Xi & Haitian Xie, 2025. "A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data," Papers 2505.22388, arXiv.org.
  • Handle: RePEc:arx:papers:2505.22388
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2505.22388
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    2. Avila-Montealegre, Oscar & Mix, Carter, 2024. "Common trade exposure and business cycle comovement," Journal of International Economics, Elsevier, vol. 152(C).
    3. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    4. Acemoglu, Daron & Johnson, Simon & Kermani, Amir & Kwak, James & Mitton, Todd, 2016. "The value of connections in turbulent times: Evidence from the United States," Journal of Financial Economics, Elsevier, vol. 121(2), pages 368-391.
    5. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    6. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2021. "The Augmented Synthetic Control Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1789-1803, October.
    7. Julian di Giovanni & Andrei A. Levchenko & Isabelle Mejean, 2018. "The Micro Origins of International Business-Cycle Comovement," American Economic Review, American Economic Association, vol. 108(1), pages 82-108, January.
    8. Laurent Gobillon & Thierry Magnac, 2016. "Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 535-551, July.
    9. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2023. "Same Root Different Leaves: Time Series and Cross‐Sectional Methods in Panel Data," Econometrica, Econometric Society, vol. 91(6), pages 2125-2154, November.
    10. Laura Mayoral, 2013. "Heterogeneous Dynamics, Aggregation, And The Persistence Of Economic Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1295-1307, November.
    11. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    12. Ziwei Mei & Peter C. B. Phillips & Zhentao Shi, 2024. "The boosted Hodrick‐Prescott filter is more general than you might think," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(7), pages 1260-1281, November.
    13. Ricardo Masini & Marcelo C. Medeiros, 2021. "Counterfactual Analysis With Artificial Controls: Inference, High Dimensions, and Nonstationarity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1773-1788, October.
    14. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    15. Asatryan, Zareh & Castellón, César & Stratmann, Thomas, 2018. "Balanced budget rules and fiscal outcomes: Evidence from historical constitutions," Journal of Public Economics, Elsevier, vol. 167(C), pages 105-119.
    16. Shi, Zhentao & Huang, Jingyi, 2023. "Forward-selected panel data approach for program evaluation," Journal of Econometrics, Elsevier, vol. 234(2), pages 512-535.
    17. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    18. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    19. 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.
    20. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    21. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    22. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    23. Giovanni Peri & Vasil Yasenov, 2019. "The Labor Market Effects of a Refugee Wave: Synthetic Control Method Meets the Mariel Boatlift," Journal of Human Resources, University of Wisconsin Press, vol. 54(2), pages 267-309.
    24. Irene Botosaru & Bruno Ferman, 2019. "On the role of covariates in the synthetic control method," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 117-130.
    25. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    26. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    27. Alberto Abadie & Alexis Diamond & Jens Hainmueller, 2015. "Comparative Politics and the Synthetic Control Method," American Journal of Political Science, John Wiley & Sons, vol. 59(2), pages 495-510, February.
    28. Alexei Onatski & Chen Wang, 2021. "Spurious Factor Analysis," Econometrica, Econometric Society, vol. 89(2), pages 591-614, March.
    29. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    30. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
    31. Laura Mayoral, 2013. "Heterogeneous Dynamics, Aggregation, And The Persistence Of Economic Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 1295-1307, November.
    32. Ibragimov, Rustam & Sharakhmetov, Shaturgun, 2002. "The exact constant in the Rosenthal inequality for random variables with mean zero," Scholarly Articles 2623703, Harvard University Department of Economics.
    33. Andreas Billmeier & Tommaso Nannicini, 2013. "Assessing Economic Liberalization Episodes: A Synthetic Control Approach," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 983-1001, July.
    34. Cheng Hsiao & H. Steve Ching & Shui Ki Wan, 2012. "A Panel Data Approach For Program Evaluation: Measuring The Benefits Of Political And Economic Integration Of Hong Kong With Mainland China," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 705-740, August.
    35. Becker, Maike & Pfeifer, Gregor & Schweikert, Karsten, 2021. "Price Effects of the Austrian Fuel Price Fixing Act: A Synthetic Control Study," Energy Economics, Elsevier, vol. 97(C).
    36. Chamon, Marcos & Garcia, Márcio & Souza, Laura, 2017. "FX interventions in Brazil: A synthetic control approach," Journal of International Economics, Elsevier, vol. 108(C), pages 157-168.
    37. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    38. Cheng Hsiao & Zhentao Shi & Qiankun Zhou, 2022. "Transformed Estimation for Panel Interactive Effects Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1831-1848, October.
    39. Carvalho, Carlos & Masini, Ricardo & Medeiros, Marcelo C., 2018. "ArCo: An artificial counterfactual approach for high-dimensional panel time-series data," Journal of Econometrics, Elsevier, vol. 207(2), pages 352-380.
    40. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    41. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    42. Bai, ChongEn & Li, Qi & Ouyang, Min, 2014. "Property taxes and home prices: A tale of two cities," Journal of Econometrics, Elsevier, vol. 180(1), pages 1-15.
    43. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    44. Eliason, Paul & Lutz, Byron, 2018. "Can fiscal rules constrain the size of government? An analysis of the “crown jewel” of tax and expenditure limitations," Journal of Public Economics, Elsevier, vol. 166(C), pages 115-144.
    45. Julius J. Andersson, 2019. "Carbon Taxes and CO2 Emissions: Sweden as a Case Study," American Economic Journal: Economic Policy, American Economic Association, vol. 11(4), pages 1-30, November.
    46. Ricardo Masini & Marcelo C. Medeiros, 2022. "Counterfactual Analysis and Inference With Nonstationary Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 227-239, January.
    47. Hou, Lei & Li, Kunpeng & Li, Qi & Ouyang, Min, 2021. "Revisiting the location of FDI in China: A panel data approach with heterogeneous shocks," Journal of Econometrics, Elsevier, vol. 221(2), pages 483-509.
    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. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    2. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    3. Michael Funke & Kadri Männasoo & Helery Tasane, 2023. "Regional Economic Impacts of the Øresund Cross-Border Fixed Link: Cui Bono?," CESifo Working Paper Series 10557, CESifo.
    4. Viviano, Davide & Bradic, Jelena, 2023. "Synthetic Learner: Model-free inference on treatments over time," Journal of Econometrics, Elsevier, vol. 234(2), pages 691-713.
    5. Nuno Garoupa & Rok Spruk, 2024. "Populist Constitutional Backsliding and Judicial Independence: Evidence from Turkiye," Papers 2410.02439, arXiv.org.
    6. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2022. "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data," Papers 2207.14481, arXiv.org, revised Oct 2022.
    7. Cummins Joseph & Miller Douglas L. & Smith Brock & Simon David, 2024. "Matching on Noise: Finite Sample Bias in the Synthetic Control Estimator," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 67-95, January.
    8. Stefano, Roberta di & Mellace, Giovanni, 2020. "The inclusive synthetic control method," Discussion Papers on Economics 14/2020, University of Southern Denmark, Department of Economics.
    9. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    10. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    11. Fry, Joseph, 2024. "A method of moments approach to asymptotically unbiased Synthetic Controls," Journal of Econometrics, Elsevier, vol. 244(1).
    12. Luis Costa & Vivek F. Farias & Patricio Foncea & Jingyuan (Donna) Gan & Ayush Garg & Ivo Rosa Montenegro & Kumarjit Pathak & Tianyi Peng & Dusan Popovic, 2023. "Generalized Synthetic Control for TestOps at ABI: Models, Algorithms, and Infrastructure," Interfaces, INFORMS, vol. 53(5), pages 336-349, September.
    13. Emery, Thomas & Mélon, Lela & Spruk, Rok, 2023. "Does e-procurement matter for economic growth? Subnational evidence from Australia," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 318-334.
    14. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    15. Pekka Malo & Juha Eskelinen & Xun Zhou & Timo Kuosmanen, 2024. "Computing Synthetic Controls Using Bilevel Optimization," Computational Economics, Springer;Society for Computational Economics, vol. 64(2), pages 1113-1136, August.
    16. Xiong, Ruoxuan & Pelger, Markus, 2023. "Large dimensional latent factor modeling with missing observations and applications to causal inference," Journal of Econometrics, Elsevier, vol. 233(1), pages 271-301.
    17. Tomasz Serwach, 2023. "The European Union and within‐country income inequalities. The case of the new member states," The World Economy, Wiley Blackwell, vol. 46(7), pages 1890-1939, July.
    18. Tomasz Serwach, 2022. "The European Union and within-country income inequalities. The case of the New Member States," Working Papers hal-03548416, HAL.
    19. Niklas Potrafke & Luisa Dörr & Klaus Gründler & Tuuli Tähtinen & Luisa Dörr, 2025. "Female Leaders and the Representation of Women in Government," CESifo Working Paper Series 11851, CESifo.
    20. Pier Basaglia & Sophie M. Behr & Moritz A. Drupp, 2023. "De-Fueling Externalities: How Tax Salience and Fuel Substitution Mediate Climate and Health Benefits," Discussion Papers of DIW Berlin 2041, DIW Berlin, German Institute for Economic Research.

    More about this item

    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:2505.22388. 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.