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Linearly Transforming Variables in the VAR Model, How Does it Change the Impulse Response?

Author

Listed:
  • Reusens Peter

    (National Bank of Belgium, De Berlaimontlaan, 14Brussels, Belgium, Tel: +32 2 221 22 56)

  • Croux Christophe

    (Faculty of Economics and Business, KU Leuven, Naamsestraat 69, B-3000 Leuven, Belgium, Tel: +32 16 32 69 58)

Abstract

This paper analyzes the impulse response function of vector autoregression models for variables that are linearly transformed. The impulse response is equal to the linear transformation of the original impulse response if and only if the shock is equal to the linear transformation of the original shock. In particular, we consider shocks in one error term only, generalized shocks, structural shocks identified by short-run recursive restrictions and structural shocks identified by long-run recursive restrictions. A vector autoregression model with expected inflation, the overnight rate and a long term ex-ante real interest rate that replaces the corresponding long term nominal interest rate, illustrates our results.

Suggested Citation

  • Reusens Peter & Croux Christophe, 2018. "Linearly Transforming Variables in the VAR Model, How Does it Change the Impulse Response?," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-16, January.
    • Handle: RePEc:bpj:jecome:v:7:y:2018:i:1:p:16:n:3
    DOI: 10.1515/jem-2015-0015
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    References listed on IDEAS

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    1. Ørjan Robstad, 2014. "House prices, credit and the effect of monetary policy in Norway: Evidence from Structural VAR Models," Working Paper 2014/05, Norges Bank.
    2. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    3. Pesaran, H. Hashem & Shin, Yongcheol, 1998. "Generalized impulse response analysis in linear multivariate models," Economics Letters, Elsevier, vol. 58(1), pages 17-29, January.
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    Keywords

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    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • 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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