IDEAS home Printed from https://ideas.repec.org/p/fip/fedkrw/91859.html
   My bibliography  Save this paper

Local Projections, Autocorrelation, and Efficiency

Author

Abstract

It is well known that Local Projections (LP) residuals are autocorrelated. Conventional wisdom says that LP have to be estimated by OLS with Newey-West (or some type of Heteroskedastic and Autocorrelation Consistent (HAC)) standard errors and that GLS is not possible because the autocorrelation process is unknown and/or because the GLS estimator would be inconsistent. I derive the autocorrelation process of LP and show that it can be corrected for using a consistent GLS estimator. Estimating LP with GLS has three major implications: 1) LP GLS can be less biased, more efficient, and generally has better coverage properties than estimation by OLS with HAC standard errors. 2) Consistency of the LP GLS estimator gives a general counterexample showing that strict exogeneity is not a necessary condition for GLS. 3) Since the autocorrelation process can be modeled explicitly, it is now possible to estimate time-varying parameter LP.

Suggested Citation

  • Amaze Lusompa, 2021. "Local Projections, Autocorrelation, and Efficiency," Research Working Paper RWP 21-01, Federal Reserve Bank of Kansas City.
    • Handle: RePEc:fip:fedkrw:91859
    DOI: 10.18651/RWP2021-01
    as

    Download full text from publisher

    File URL: https://www.kansascityfed.org/documents/7865/rwp21-01.pdf
    File Function: Full text
    Download Restriction: no
    File URL: https://www.kansascityfed.org/research/research-working-papers/local-projections-autocorrelation-efficiency/
    Download Restriction: no
    File URL: https://libkey.io/10.18651/RWP2021-01?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "The Transmission of Monetary Policy Shocks," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 74-107, July.
    2. 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.
    3. Christiane Baumeister & Gert Peersman, 2013. "The Role Of Time‐Varying Price Elasticities In Accounting For Volatility Changes In The Crude Oil Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1087-1109, November.
    4. Koop, Gary & Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Bayesian compressed vector autoregressions," Journal of Econometrics, Elsevier, vol. 210(1), pages 135-154.
    5. Berkowitz, J. & Birgean, I. & Kilian, L., 1999. "On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series," Papers 99-01, Michigan - Center for Research on Economic & Social Theory.
    6. 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.
    7. Zoey Yi Zhao & Meng Xie & Mike West, 2016. "Dynamic dependence networks: Financial time series forecasting and portfolio decisions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(3), pages 311-332, May.
    8. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    9. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    10. Koop, Gary & Korobilis, Dimitris, 2013. "Large time-varying parameter VARs," Journal of Econometrics, Elsevier, vol. 177(2), pages 185-198.
    11. James H. Stock & Mark W. Watson, 2018. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments," Economic Journal, Royal Economic Society, vol. 128(610), pages 917-948, May.
    12. Lopes, Hedibert Freitas & Moreira, Ajax R. Bello & Schmidt, Alexandra Mello, 1999. "Hyperparameter estimation in forecast models," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 387-410, February.
    13. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    14. Elena Pesavento & Barbara Rossi, 2006. "Small‐sample confidence intervals for multivariate impulse response functions at long horizons," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1135-1155, December.
    15. Òscar Jordà & Sharon Kozicki, 2011. "Estimation And Inference By The Method Of Projection Minimum Distance: An Application To The New Keynesian Hybrid Phillips Curve," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(2), pages 461-487, May.
    16. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    17. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2019. "Priors for the Long Run," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 565-580, April.
    18. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    19. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
    20. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    21. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    22. Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-446, October.
    23. Gary Koop, 2017. "Bayesian Methods for Empirical Macroeconomics," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 9(1), pages 33-56, June.
    24. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    25. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    26. Granger Clive W.J., 2008. "Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-11, September.
    27. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    28. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    29. Emi Nakamura & Jón Steinsson, 2018. "Identification in Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 59-86, Summer.
    30. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    31. 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.
    32. Lutz Kilian & Yun Jung Kim, 2011. "How Reliable Are Local Projection Estimators of Impulse Responses?," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1460-1466, November.
    33. Alun Lloyd Pope, 1990. "Biases Of Estimators In Multivariate Non‐Gaussian Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 249-258, May.
    34. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    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. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Identification and Inference Under Narrative Restrictions," Papers 2102.06456, arXiv.org.
    2. Jörg Breitung & Ralf Brüggemann, 2019. "Projection estimators for structural impulse responses," Working Paper Series of the Department of Economics, University of Konstanz 2019-05, Department of Economics, University of Konstanz.
    3. Leonardo Nogueira Ferreira, 2023. "Monetary Policy Surprises, Financial Conditions, and the String Theory Revisited," Working Papers Series 573, Central Bank of Brazil, Research Department.
    4. Bruns, Martin & Lütkepohl, Helmut, 2022. "Comparison of local projection estimators for proxy vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    5. Oscar Jorda & Alan Taylor & Sanjay Singh, 2019. "The Long-Run Effects of Monetary Policy," 2019 Meeting Papers 1307, Society for Economic Dynamics.
    6. Philippe Goulet Coulombe, 2020. "Time-Varying Parameters as Ridge Regressions," Papers 2009.00401, arXiv.org, revised Apr 2023.

    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. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    2. Mikkel Plagborg‐Møller & Christian K. Wolf, 2021. "Local Projections and VARs Estimate the Same Impulse Responses," Econometrica, Econometric Society, vol. 89(2), pages 955-980, March.
    3. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    4. Francisco Serranito & Philipp RODERWEIS & Jamel Saadaoui, 2023. "Is Quantitative Easing Productive? The Role of Bank Lending in the Monetary Transmission Process," EconomiX Working Papers 2023-17, University of Paris Nanterre, EconomiX.
    5. 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.
    6. Dimitrios P. Louzis, 2019. "Steady‐state modeling and macroeconomic forecasting quality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 285-314, March.
    7. Dake Li & Mikkel Plagborg-M{o}ller & Christian K. Wolf, 2021. "Local Projections vs. VARs: Lessons From Thousands of DGPs," Papers 2104.00655, arXiv.org, revised Jan 2024.
    8. Luca Brugnolini, 2018. "About Local Projection Impulse Response Function Reliability," CEIS Research Paper 440, Tor Vergata University, CEIS, revised 09 Jun 2018.
    9. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2021. "Local Projection Inference Is Simpler and More Robust Than You Think," Econometrica, Econometric Society, vol. 89(4), pages 1789-1823, July.
    10. Tsionas, Mike G. & Izzeldin, Marwan & Trapani, Lorenzo, 2022. "Estimation of large dimensional time varying VARs using copulas," European Economic Review, Elsevier, vol. 141(C).
    11. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    12. Oscar Jorda & Alan Taylor & Sanjay Singh, 2019. "The Long-Run Effects of Monetary Policy," 2019 Meeting Papers 1307, Society for Economic Dynamics.
    13. Cimadomo, Jacopo & Giannone, Domenico & Lenza, Michele & Monti, Francesca & Sokol, Andrej, 2022. "Nowcasting with large Bayesian vector autoregressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 500-519.
    14. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    15. Koop, Gary & Korobilis, Dimitris & Pettenuzzo, Davide, 2019. "Bayesian compressed vector autoregressions," Journal of Econometrics, Elsevier, vol. 210(1), pages 135-154.
    16. Philippe Goulet Coulombe, 2020. "The Macroeconomy as a Random Forest," Papers 2006.12724, arXiv.org, revised Mar 2021.
    17. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    18. Hacioglu Hoke, Sinem, 2019. "Macroeconomic effects of political risk shocks," Bank of England working papers 841, Bank of England.
    19. Gary Koop, 2012. "Using VARs and TVP-VARs with Many Macroeconomic Variables," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(3), pages 143-167, September.
    20. repec:spo:wpmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    21. Nima Nonejad, 2021. "An Overview Of Dynamic Model Averaging Techniques In Time‐Series Econometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 35(2), pages 566-614, April.
    22. Pestova, Anna & Mamonov, Mikhail, 2019. "Should we care? : The economic effects of financial sanctions on the Russian economy," BOFIT Discussion Papers 13/2019, Bank of Finland, Institute for Economies in Transition.

    More about this item

    Keywords

    Local Projections; Generalized Least Squares;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

    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:fip:fedkrw:91859. 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: Zach Kastens (email available below). General contact details of provider: https://edirc.repec.org/data/frbkcus.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.