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Local Projections, Autocorrelation, and Efficiency

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  • Lusompa, Amaze

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 and West (1987) (or some type of Heteroskedastic and Autocorrelation Consistent (HAC)) standard errors and that GLS is not possible because the autocorrelation process is unknown. I show that the autocorrelation process of LP is known and that autocorrelation can be corrected for using GLS. Estimating LP with GLS has three major implications: 1) LP GLS can be substantially more efficient and less biased than estimation by OLS with Newey-West standard errors. 2) Since the autocorrelation process can be modeled explicitly, it is possible to give a fully Bayesian treatment of LP. That is, LP can be estimated using frequentist/classical or fully Bayesian methods. 3) Since the autocorrelation process can be modeled explicitly, it is now possible to estimate time-varying parameter LP.

Suggested Citation

  • Lusompa, Amaze, 2019. "Local Projections, Autocorrelation, and Efficiency," MPRA Paper 99856, University Library of Munich, Germany, revised 11 Apr 2020.
    • Handle: RePEc:pra:mprapa:99856
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    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.

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    More about this item

    Keywords

    Impulse Response; Local Projections; Autocorrelation; GLS;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • 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

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