# Analysing Monetary Policy Shocks by Sign and Parametric Restrictions: The Evidence from Russia

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. The Concept of SVARs

_{1}denotes n × k matrices of coefficients, ${\mathrm{z}}_{\mathrm{t}}$ is an n × 1 vector of variables, and e

_{t}is a reduced form of shock with zero mean expectation and constant covariance matrices without serial correlations. This leads to the SVAR representation of the variables:

_{k}represents the kth lag impulse response of ${\mathrm{z}}_{\mathrm{t}+\mathrm{k}}$ to a unit change in e

_{t}. Thus, the MA representation of SVAR is

_{t+k}are calculated by ${\mathrm{C}}_{\mathrm{k}}={\mathrm{D}}_{\mathrm{k}}{\mathrm{B}}_{0}^{-1}$.

#### 3.3. Sign Restricted SVARS for Open Economy

_{t}), inflation (π

_{t}), and output gap (y

_{t}). Therefore, the model we used is based on the equation systems given below (Ouliaris et al. 2016):

_{t}) = Ω

_{R}with unit variances. One might attain uncorrelated shocks y

_{t}= Pe

_{t}, by using CD (Cholesky decomposition) or SVD (singular value decomposition). According to CD, A is a triangular matrix, Ω

_{R}= AA’; thus, (A’)

^{−1}= P provides uncorrelated shocks that can be converted to shocks with unit variance. Similarly, for SVD, the process proceeds as Ω

_{R}= UFU’, where UU’ = I, UU’ = F. Setting diagonal matrix P = U’ will produce uncorrelated shock by matrix F, and similarly, it can be expressed in terms of unit variances. After obtaining these variances, it is possible to obtain IRs of them, and this allows us to recombine the initial set. Furthermore, IRs might be attainable by a square matrix Q, featured QQ’ = I

_{n}to provide uncorrelated innovations. There is more than one suggestion for the derivation of Q matrices including the Givens matrices. Those who maintain IRs consort with sign restrictions. Another way is offered by Rubio-Ramirez et al. (2010), who use a simulation algorithm that has limited features. In the aforementioned practices, Q matrix applications cannot be practised with both short and long-term parametric SVAR restrictions. The SRR approach is based on recombining sign restriction initial information by reconsolidating Givens and Householder approaches to build a new set of orthogonal shocks. The primary standardized innovations are reproduced to develop a fresh set of innovations, from which an extra set of impulse responses is obtained and decided against the signs. The process of generating multiple responses is repeated many times until the system protects those that meet the sign constraints.

_{1t}as the instrument for y

_{t}to attain e

_{2t.}The same procedure should be applied to Equation (7) using e

_{1t}and e

_{2t}on behalf of y

_{t}and π

_{t}to obtain e

_{3t}. To create the widest potential variety of impulse responses, in respect of sign restrictions, the values of the coefficients generated as in the work of

## 4. Empirical Analysis

#### 4.1. Preliminary Tests

#### 4.2. Variance Decomposition and Median Responses

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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Variable/Shocks | Demand | Cost–Push | Monetary Policy |
---|---|---|---|

y_{t} | + | − | − |

π_{t} | + | + | − |

i_{t} | + | + | + |

INFL | INT | GAP | |
---|---|---|---|

Mean | 3.78 | 2.28 | 0.01 |

Median | 3.92 | 2.17 | 0.02 |

Maximum | 4.74 | 3.53 | 0.07 |

Minimum | 1.92 | 1.44 | −0.08 |

Std. Dev. | 0.77 | 0.51 | 0.02 |

Jarque-Bera | 10.5 | 8.85 | 7.25 |

Probability | 0.00 | 0.01 | 0.02 |

Observations | 87 | 87 | 87 |

Lag Length | AIC | SC | HQ | LM Test Result | Portmanteau Test Results |
---|---|---|---|---|---|

1 | −10.20 | −9.93 | −10.14 | Serial Correlation | — |

2 | −11.04 | −10.44 * | −10.80 | Serial Correlation | — |

3 | −11.29 * | −10.42 | −10.94 * | No Serial Correlation | — |

4 | −11.225 | −10.10 | −10.77 | No Serial Correlation | No Serial Correlation |

Variables | Levels | First Differences | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

ADF None | ADF Int. | PP None | PP Int. | KPSS Int. | ADF None | ADF Int. | PP None | PP Int. | KPSS Int. | |

INFL | 1.43 | −5.99 * | 3.08 | −4.05 * | 1.12 | −1.99 *** | −3.06 * | −2.90 * | −3.78 * | 0.61 *** |

INT | −1.31 | −2.67 *** | −1.31 | −2.70 *** | 0.47 *** | −8.26 * | −8.24 * | −8.26 * | −8.25 * | 0.13 |

GAP | −4.37 * | −4.35 * | −3.54 * | −3.53 * | 0.03 | −5.67 * | −5.64 * | −5.73 * | −5.70 * | 0.06 |

Variable/Shock | Time | Demand | Supply | MP |
---|---|---|---|---|

GAP | 2 | 93 | 6 | 1 |

5 | 82 | 15 | 3 | |

8 | 80 | 16 | 4 | |

10 | 79 | 18 | 3 | |

Inflation | 2 | 9 | 90 | 1 |

5 | 25 | 71 | 4 | |

8 | 25 | 70 | 5 | |

10 | 22 | 71 | 6 | |

Interest | 2 | 10 | 3 | 87 |

5 | 10 | 12 | 77 | |

8 | 19 | 20 | 61 | |

10 | 23 | 22 | 55 |

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**MDPI and ACS Style**

Yıldız, B.F.; Gökmenoğlu, K.K.; Wong, W.-K.
Analysing Monetary Policy Shocks by Sign and Parametric Restrictions: The Evidence from Russia. *Economies* **2022**, *10*, 239.
https://doi.org/10.3390/economies10100239

**AMA Style**

Yıldız BF, Gökmenoğlu KK, Wong W-K.
Analysing Monetary Policy Shocks by Sign and Parametric Restrictions: The Evidence from Russia. *Economies*. 2022; 10(10):239.
https://doi.org/10.3390/economies10100239

**Chicago/Turabian Style**

Yıldız, Bünyamin Fuat, Korhan K. Gökmenoğlu, and Wing-Keung Wong.
2022. "Analysing Monetary Policy Shocks by Sign and Parametric Restrictions: The Evidence from Russia" *Economies* 10, no. 10: 239.
https://doi.org/10.3390/economies10100239