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Comparing external and internal instruments for vector autoregressions

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  • Bruns, Martin
  • Lütkepohl, Helmut

Abstract

In conventional proxy VAR analysis, the shocks of interest are identified by external instruments. This is typically accomplished by considering the covariance of the instruments and the reduced-form residuals. Alternatively, the instruments may be internalized by augmenting the VAR process by the instruments or proxies. These alternative identification methods are compared and it is shown that the resulting shocks obtained with the alternative approaches differ in general. Conditions are provided under which their impulse responses are nevertheless identical. If the conditions are satisfied, identification of the shocks is ensured. An empirical example illustrates the theoretical results.

Suggested Citation

  • Bruns, Martin & Lütkepohl, Helmut, 2025. "Comparing external and internal instruments for vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:dyncon:v:177:y:2025:i:c:s0165188925000971
    DOI: 10.1016/j.jedc.2025.105131
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    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

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