# Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{o}: $\beta =1$. However, the literature confirms that there are several points that should be considered to accurately estimate this parameter and to test this hypothesis. Our study proposes a different statistical methodology to test the relationship between inflation and the nominal interest rate, adding to the controversy over which technique is the most suitable for testing the Fisher effect. 1 Here, we consider the appropriate treatment of the time series properties of the variables, as well as the possible presence of changes in the values of the parameters α and β. In this study, we consider the importance of these two points.

## 2. Fisher Effect with Non-Integrated Variables

#### 2.1. Analysis of the Time Properties of the Nominal Interest Rates and Inflation Rates

^{GLS}, which is based on the very popular ADF test. Following Elliot et al. (1996) [36], this can be obtained by estimating the following model:

^{GLS}is based on the use of GLS (Generalized Least Squares) estimation methods instead of OLS (Ordinary Least Squares) estimators and on determining the value of the lag truncation parameter (ℓ) by using an information criterion, called MIC (Modified Information Criteria), also proposed in Ng and Perron (2001) [35]. This type of statistics is not useful to reject the presence of a unit root in nominal interest rates and inflation. This is why some authors have recently employed different statistics to analyze the time series properties of the variables to take advantage of the cross-sectional information of a database. Thus, it seems suitable to use a panel data approach to test for the presence of a unit root in the variables in the Fisher equation. In order to select the most appropriate type of panel data unit root test, we should first know the characteristics of the database, because of the possible presence of a cross-sectional correlation between the variables.

_{o}:${\alpha}_{i}=0$ in the following cross-sectional ADF regressions:

#### 2.2. Empirical Evidence from the G7 Countries

## 3. Structural Breaks and the Fisher Effect

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

^{2.}In our present case, we only include an intercept in the model specification.^{3.}The Italian short-term interest rates for 1970:Q1–1970:Q4 were estimated using the evolution of Italy’s long-term interest rates.^{4.}See Pesaran (2012) [39] in this regard.^{6.}This hypothesis has recently been re-examined with optimizing agents in an overlapping generations context. See Rapach (2003) [59] for a comprehensive survey.^{7.}In order to analyze the robustness of the estimated periods, we have obtained the Bai–Perron statistics for the 1980:Q1–2015:Q4 and for the 1970:Q1–2007:Q4 samples. In this latter case, the estimated periods of breaks almost coincide with those of the full sample. In the former, the variations are a bit larger, especially for the short-run case. The total number of estimated breaks is 19, 15 being coincident with the full sample analysis. For the long-run model, the new total of estimated breaks is 23, 20 being coincident. In summary, given this high degree of coincidence in the results and taking into account that these new estimated breaks are a consequence of the decrease in the size of the lowest segment, we can conclude that the Bai–Perron procedure offers very robust results in this scenario.

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**Figure 1.**(

**a**) Expected Inflation rates; (

**b**) Long-run nominal interest rates; (

**c**) Short-run nominal interest rates.

**Figure 2.**Estimated Fisher Coefficient. Long-run nominal interest rate. The solid line represents the estimated Fisher coefficient defined by (9), whilst the dotted line reflects twice the standard deviation, obtained by way of bootstrapping techniques.

**Figure 3.**Estimated Fisher Coefficient. Short-run nominal interest rate. The solid line represents the estimated Fisher coefficient defined by (9), whilst the dotted line reflects twice the standard deviation, obtained by way of the bootstrapping techniques.

Long-Run Nominal Interest | Short-Run Nominal Interest | Inflation | |
---|---|---|---|

p = 0 | 29.25 * | 19.13 * | 20.06 * |

p = 1 | 26.33 * | 15.39 * | 20.32 * |

p = 2 | 25.85 * | 15.52 * | 19.27 * |

p = 3 | 25.16 * | 15.32 * | 19.83 * |

p = 4 | 24.76 * | 15.28 * | 18.78 * |

Long-Run Nominal Interest | Short-Run Nominal Interest | Inflation | |
---|---|---|---|

p = 0 | −2.89 ** | −6.73** | −12.94 ** |

p = 1 | −3.08 ** | −7.19** | −12.46 ** |

p = 2 | −2.27 * | −6.14** | −10.79 ** |

p = 3 | −2.38 ** | −5.67** | −7.52 ** |

p = 4 | −2.36 ** | −5.87** | −7.50 ** |

${\mathit{WD}}_{\mathit{max}}^{\mathbf{0.05}}$ | ψ_{1} | TB1 | ψ_{2} | TB2 | ψ_{3} | TB3 | ψ_{4} | TB4 | ψ_{5} | TB5 | ψ_{6} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Panel A: long-run nominal interest rates | ||||||||||||

Canada | 616 | 0.53 | 79:2 | 0.61 | 86:1 | 0.42 | 96:3 | 0.63 | 07:4 | 0.18 | - | - |

France | 258 | 0.61 | 79:4 | 1.37 | 86:3 | 1.11 ^{$} | 96:3 | 0.68 | 09:1 | 1.02 | - | - |

Germany | 178 | 0.40 | 96:3 | 0.73 | 08:4 | 1.50 | - | - | - | - | - | - |

Italy | 218 | 0.95 | 76:3 | 1.27 ^{$} | 84:2 | 1.52 | 97:2 | 1.15 | - | - | - | - |

Japan | 1337 | 0.20 | 85:2 | 0.47 | 95:1 | 0.07 | 01:4 | 0.71 | - | - | - | - |

UK | 495 | 0.67 | 76:3 | 0.13 | 83:2 | 0.24 | 91:3 | 0.86 | 98:2 | 0.07 | 08:4 | 0.50 |

USA | 254 | 0.52 | 78:4 | 2.63 ^{$} | 85:4 | 0.62 | 92:2 | 0.99 | 00:4 | 0.12 | 08:3 | 0.38 |

Panel B: short-run nominal interest rates | ||||||||||||

Canada | 642 | 0.86 | 79:1 | 0.89 | 92:1 | 0.15 | 08:4 | 0.08 | - | - | - | - |

France | 375 | 0.86 ^{$} | 81:1 | 0.68 | 95:3 | 0.03 | 08:4 | 0.31 | - | - | - | - |

Germany | 185 | 0.70 | 95:3 | 0.92 | 09:1 | 0.40 | - | - | - | - | - | - |

Italy | 586 | 0.80 | 79:4 | 0.79 | 86:3 | 1.75 | 98:3 | 1.71 | - | - | - | - |

Japan | 266 | 0.55 | 92:4 | 0.13 | - | - | - | - | - | - | - | - |

UK | 526 | 0.08 | 79:2 | 0.53 | 92:3 | 0.10 | 08:4 | 0.03 | - | - | - | - |

USA | 500 | 0.71 | 79:2 | 0.92 | 86:1 | 1.43 | 01:3 | −0.70 | 08:4 | −0.01 | - | - |

^{$}means that a second order ARDL (Autoregressive Distributed Lag) model was estimated.

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**MDPI and ACS Style**

Clemente, J.; Gadea, M.D.; Montañés, A.; Reyes, M.
Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries. *Econometrics* **2017**, *5*, 11.
https://doi.org/10.3390/econometrics5010011

**AMA Style**

Clemente J, Gadea MD, Montañés A, Reyes M.
Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries. *Econometrics*. 2017; 5(1):11.
https://doi.org/10.3390/econometrics5010011

**Chicago/Turabian Style**

Clemente, Jesús, María Dolores Gadea, Antonio Montañés, and Marcelo Reyes.
2017. "Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries" *Econometrics* 5, no. 1: 11.
https://doi.org/10.3390/econometrics5010011