## 1 Introduction

^{1}

^{2}Panels 1a and 1b compare the unconditional variances of inflation deviations from an estimated target and the output gap for Euro Area countries and non-Euro OECD countries over three periods: beginning of the Great Moderation until inception of the Euro, start of the Euro until the period of Issing’s (2005) judgment roughly before the beginning of the Great Recession, and, the crisis period since then. The panels suggest that, according to these key indicators of macroeconomic performance, non-Euro OECD countries have been more successful in reducing inflation and output variability after the start of the Euro. Moreover, they have been more successful in stabilizing both inflation and output variability during the most recent period. However, this kind of evidence leaves many questions unanswered. Do these results depend on different shocks hitting the two country groups? Are they uniform across Euro countries, time or policy changes? In this paper, we address these questions through an empirical set-up drawing from both counterfactual analysis and the analysis of productive processes.

^{3}Moreover, Ball (2010) finds that the Euro adoption had no significant effects on indicators of macroeconomic performance such as the level or variability of inflation or GDP. Nevertheless, the focus of Ball (2010) is on the effects of adopting inflation targeting (IT). In fact, the bulk of the empirical literature that quantifies the effect of a change in the monetary regime on macroeconomic performance focuses on IT. Two key themes in this literature stand out: first, this literature quantifies the effect of a change in the monetary regime on the moment of a single variable, e.g., the variability of inflation or GDP; second, a key challenge in this literature is endogeneity, as it is unanimously recognized that the choice of IT is affected by initial conditions.

^{4}Hence from the standpoint of such a framework, evidence based on the variability of inflation or output in isolation appears problematic. In case such research finds lower inflation variability for Euro Area countries compared to other countries, this might simply imply that the Euro Area countries are located on a different position of the inflation output variability tradeoff, but do not face an improved tradeoff due to the Euro.

^{5}

## 2 Theoretical framework

^{6}Under optimal discretionary monetary policy (as elaborated in Clarida et al. 1999), the central bank minimizes (1) subject to the aggregate economy in each period. One can show that the minimum state variable solution of this model then implies the following long-run relationships in unconditional variances

^{7}In short, (2) to (3) show that both the optimal variances of inflation and output gap depend on the supply shock variance. Moreover, one can verify that the larger the central banks’ preference for output gap stabilization, \(\omega _{x}\), the lower \(\sigma ^{2}_{x,*}\) and the larger \(\sigma ^{2}_{\pi ,*}\).

^{8}Actual observed variability in inflation and the output gap will routinely indicate that the economy is to the right of an estimated efficient inflation output variability tradeoff, \({\textrm{Fed}}_{\textrm{actual}}\) in Fig. 2a. Therefore a central bank’s monetary policy can be classified as sub-optimal.

^{9}

^{10}

^{11}Thus, there exists an inflation output variability tradeoff, although the latter is based on the simple interest rate rule (4). The challenge is then to develop an empirical framework that is flexible enough to encompass both the tradeoffs implied by optimal and simple monetary policy.

## 3 Empirical implementation

^{12}

### 3.1 Data and estimation of structural shocks

^{13}Finally, for the Euro Area countries, we use the money market rate until 1998Q4. Then, up to 2004Q3, we use the common ECB refinancing rate, and thereafter we use the Euro Shadow Rate developed by Wu and Xia (2016). For the non-Euro OECD countries other than the UK or the US, we use the money market rate up to 2004Q3, and then, since afterwards no shadow rate is available, we use a quarterly measure of the overnight bank rate.

^{14}

^{15}

### 3.2 Identification of the effect of the Euro on macroeconomic performance

Baseline choice of periods | ||||
---|---|---|---|---|

Period | From | To | # of Obs. | Comments |

1 | 1985Q1 | 1988Q2 | 14 | Beginning of the Great Moderation |

2 | 1988Q3 | 1991Q4 | 14 | |

3 | 1992Q1 | 1995Q2 | 14 | |

4 | 1995Q3 | 1998Q4 | 14 | |

5 | 1999Q1 | 2002Q2 | 14 | Start of the Euro |

6 | 2002Q3 | 2005Q4 | 14 | |

7 | 2006Q1 | 2009Q2 | 14 | Financial Crisis |

8 | 2009Q3 | 2012Q2 | 12 | European Sovereign Debt Crisis |

9 | 2012Q3 | 2016Q1 | 15 | European Sovereign Debt Crisis (continued) |

Draghi announcement (July 26th, 2012) | ||||

Outright Monetary Transactions (OMTs) announcement (September 6th, 2012) | ||||

Expanded Asset Purchase Programme (EAPP) (January 22nd, 2015) | ||||

10 | 2016Q2 | 2019Q4 | 15 |

^{16}

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(9) | (11) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.605** | \(-\)0.561* | \(-\)0.665* | |||

(0.269) | (0.300) | (0.356) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.590* | \(-\)0.636* | \(-\)0.472 | |||

(0.295) | (0.340) | (0.410) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.390 | \(-\)0.629 | \(-\)0.089 | |||

(0.365) | (0.482) | (0.370) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.748* | \(-\)0.671 | \(-\)0.838 | |||

(0.421) | (0.457) | (0.541) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)1.054*** | \(-\)1.032** | \(-\)1.062** | |||

(0.383) | (0.408) | (0.446) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.570 | \(-\)0.200 | \(-\)1.344*** | |||

(0.333) | (0.371) | (0.281) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.287 | \(-\)0.329 | \(-\)0.363 | |||

(0.292) | (0.203) | (0.647) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.460*** | \(-\)0.461*** | \(-\)0.489*** | \(-\)0.458*** | ||

(0.083) | (0.083) | (0.084) | (0.088) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.204** | \(-\)0.209* | \(-\)0.156 | \(-\)0.156 | ||

(0.097) | (0.106) | (0.100) | (0.106) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | 0.383** | 0.380* | 0.368* | 0.265 | ||

(0.182) | (0.185) | (0.199) | (0.181) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.387*** | \(-\)0.383*** | \(-\)0.347*** | \(-\)0.348*** | ||

(0.093) | (0.098) | (0.114) | (0.110) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | \(-\)0.215 | \(-\)0.218 | \(-\)0.195 | \(-\)0.133 | ||

(0.150) | (0.151) | (0.170) | (0.164) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.545*** | 0.543*** | 0.569*** | 0.535*** | ||

(0.027) | (0.028) | (0.033) | (0.039) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | \(-\)0.030 | \(-\)0.029 | \(-\)0.019 | 0.011 | ||

(0.019) | (0.021) | (0.018) | (0.026) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | 0.039 | 0.037 | 0.030 | 0.004 | ||

(0.039) | (0.037) | (0.041) | (0.034) | ||||

\(\ln (\sigma ^{2}_{g,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.173*** | \(-\)0.171*** | \(-\)0.169*** | \(-\)0.125*** | ||

(0.053) | (0.055) | (0.054) | (0.054) | ||||

Country fixed effect | Yes | Yes | Yes | Yes | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 200 | 200 | 200 | 200 | |||

\(R^{2}\) | 0.853 | 0.853 | 0.857 | 0.867 | |||

Specification \(\hbox {tests}^{b}\): | |||||||

Ramsey (1969) Reset | 0.146 | 0.132 | 0.188 | 0.290 | |||

\(\beta _{{\mathcal {E}},-3} = \beta _{{\mathcal {E}},-2} = \beta _{{\mathcal {E}},-1}=0\) | 0.674 | 0.531 | |||||

\(\beta _{{\mathcal {E}},0} = \beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) | 0.016 | 0.001 |

^{17}

## 4 Main results

^{18}Second, the coefficient \({\hat{\alpha }}_{e}\) shows that the variance of the supply shock has a highly significant impact on the location of the tradeoff in all the Euro Area, the core and the periphery. It has a negative sign, \({\hat{\alpha }}_{e} < 0\), therefore, the larger the variance of the supply shock, the larger the variance of inflation and the output gap.

^{19}Finally, demand shocks appear to have some impact on the location of the tradeoff in all the Euro Area, the core and the periphery. In sum, the significant coefficient estimates are evidence for the existence of an inflation output variability tradeoff for the Euro Area consistent with the theoretical tradeoff discussed in Sect. 2.

^{20}We interpret these findings as evidence that the impact of the Euro adoption has changed over time. The inflation output variability tradeoff for the Euro Area countries is worse during the crisis period (relative to the control group) until the ECB’s 2012 policy turnaround, but not thereafter. The coefficient estimates can be interpreted as follows: \(\exp ({\hat{\beta }}_{{\mathcal {E}},0}) \approx 0.55\), \(\exp ({\hat{\beta }}_{{\mathcal {E}},2}) \approx 0.47\), \(\exp ({\hat{\beta }}_{{\mathcal {E}},3}) \approx 0.35\), and \(\exp ({\hat{\beta }}_{{\mathcal {E}},4}) \approx 0.57\) imply that the Euro Area had a joint variance of inflation and output, which is more than \(80\%\) (\(111\%\), \(187\%\), \(77\%\)) larger during 1999Q1 to 2002Q2 (2006Q1 to 2009Q2, 2009Q3 to 2012Q2, 2012Q3 to 2016Q1) compared to the control group.

^{21}

## 5 Robustness

^{22}

### 5.1 Lagged dependent variable approach

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(12) | (14) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.537** | \(-\)0.308* | \(-\)0.776*** | |||

(0.199) | (0.174) | (0.236) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.672** | \(-\)0.544** | \(-\)0.638 | |||

(0.321) | (0.306) | (0.370) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.362 | \(-\)0.401 | \(-\)0.202 | |||

(0.309) | (0.300) | (0.404) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.403 | \(-\)0.105 | \(-\)0.791** | |||

(0.292) | (0.308) | (0.309) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)0.857** | \(-\)0.673* | \(-\)1.126*** | |||

(0.333) | (0.368) | (0.338) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.635** | \(-\)0.113 | \(-\)1.721*** | |||

(0.284) | (0.264) | (0.205) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.252 | \(-\)0.282 | \(-\)0.439 | |||

(0.337) | (0.271) | (0.523) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.408*** | \(-\)0.441*** | \(-\)0.424*** | \(-\)0.406*** | ||

(0.083) | (0.091) | (0.099) | (0.104) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.538*** | \(-\)0.515*** | \(-\)0.507** | \(-\)0.489** | ||

(0.156) | (0.148) | (0.192) | (0.187) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | 0.400* | 0.366 | 0.457** | 0.279 | ||

(0.228) | (0.224) | (0.215) | (0.176) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.332*** | \(-\)0.314** | \(-\)0.315** | \(-\)0.299** | ||

(0.107) | (0.117) | (0.121) | (0.141) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | \(-\)0.439*** | \(-\)0.469*** | \(-\)0.455*** | \(-\)0.380** | ||

(0.130) | (0.132) | (0.156) | (0.143) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.599*** | 0.588*** | 0.625*** | 0.575*** | ||

(0.041) | (0.043) | (0.049) | (0.052) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | 0.007 | \(-\)0.002 | 0.025 | 0.065* | ||

(0.025) | (0.025) | (0.027) | (0.036) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | 0.067* | 0.061 | 0.063* | 0.018 | ||

(0.038) | (0.037) | (0.036) | (0.028) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.112 | \(-\)0.112 | \(-\)0.099 | \(-\)0.016 | ||

(0.071) | (0.070) | (0.072) | (0.066) | ||||

Country fixed effect | No | No | No | No | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 120 | 120 | 120 | 120 | |||

\(R^{2}\) | 0.892 | 0.897 | 0.897 | 0.918 | |||

Specification \(\hbox {tests}^{\textrm{b}}\): | |||||||

Ramsey (1969) Reset | 0.048 | 0.026 | 0.075 | 0.204 | |||

\(\beta _{{\mathcal {E}},-3}=\beta _{{\mathcal {E}},-2} = \beta _{{\mathcal {E}},-1}=0\) | |||||||

\(\beta _{{\mathcal {E}},0} =\beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) |

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(9) | (11) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.428* | \(-\)0.378 | \(-\)0.507* | |||

(0.213) | (0.243) | (0.262) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.490* | \(-\)0.530 | \(-\)0.462 | |||

(0.270) | (0.330) | (0.322) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.285 | \(-\)0.476 | \(-\)0.009 | |||

(0.281) | (0.356) | (0.312) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.666* | \(-\)0.710* | \(-\)0.550 | |||

(0.340) | (0.346) | (0.433) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)0.562* | \(-\)0.575* | \(-\)0.489 | |||

(0.314) | (0.309) | (0.444) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.272 | 0.192 | \(-\)1.322*** | |||

(0.420) | (0.455) | (0.418) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.195 | \(-\)0.204 | \(-\)0.401 | |||

(0.314) | (0.278) | (0.533) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.385*** | \(-\)0.386*** | \(-\)0.387*** | \(-\)0.356*** | ||

(0.058) | (0.057) | (0.059) | (0.060) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.206** | \(-\)0.211** | \(-\)0.189* | \(-\)0.186** | ||

(0.091) | (0.089) | (0.096) | (0.085) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | 0.321 | 0.309 | 0.304 | 0.319 | ||

(0.207) | (0.204) | (0.227) | (0.206) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.210* | \(-\)0.206* | \(-\)0.194 | \(-\)0.232** | ||

(0.103) | (0.100) | (0.118) | (0.108) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | \(-\)0.095 | \(-\)0.091 | \(-\)0.052 | \(-\)0.067 | ||

(0.147) | (0.148) | (0.161) | (0.155) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.492*** | 0.491*** | 0.500*** | 0.445*** | ||

(0.053) | (0.053) | (0.056) | (0.058) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | 0.074*** | 0.074*** | 0.070** | 0.092*** | ||

(0.025) | (0.025) | (0.026) | (0.030) | ||||

\(\ln (\sigma ^{2}_{e,i,t})\times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | 0.023 | 0.019 | 0.014 | \(-\)0.021 | ||

(0.062) | (0.061) | (0.063) | (0.054) | ||||

\(\ln (\sigma ^{2}_{g,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.118* | \(-\)0.113 | \(-\)0.130* | \(-\)0.105** | ||

(0.068) | (0.067) | (0.064) | (0.044) | ||||

Country fixed effect | Yes | Yes | Yes | Yes | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 200 | 200 | 200 | 200 | |||

\(R^{2}\) | 0.854 | 0.855 | 0.857 | 0.873 | |||

Specification \(\hbox {tests}^{\textrm{b}}\): | |||||||

Ramsey (1969) Reset | 0.526 | 0.561 | 0.702 | 0.827 | |||

\(\beta _{{\mathcal {E}},-3}=\beta _{{\mathcal {E}},-2} = \beta _{{\mathcal {E}},-1}=0\) | 0.754 | 0.771 | |||||

\(\beta _{{\mathcal {E}},0} =\beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) | 0.319 | 0.135 |

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(12) | (14) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.550** | \(-\)0.308 | \(-\)0.675*** | |||

(0.235) | (0.257) | (0.149) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.660* | \(-\)0.566 | \(-\)0.756** | |||

(0.371) | (0.414) | (0.318) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.460 | \(-\)0.517 | \(-\)0.248 | |||

(0.319) | (0.347) | (0.445) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.617** | \(-\)0.441 | \(-\)0.694** | |||

(0.277) | (0.334) | (0.255) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)0.618** | \(-\)0.502 | \(-\)0.551 | |||

(0.245) | (0.335) | (0.352) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.395 | 0.156 | \(-\)1.623*** | |||

(0.525) | (0.528) | (0.399) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.422 | \(-\)0.339 | \(-\)0.816** | |||

(0.321) | (0.357) | (0.321) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.552*** | \(-\)0.568*** | \(-\)0.549*** | \(-\)0.499*** | ||

(0.079) | (0.078) | (0.081) | (0.091) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.383*** | \(-\)0.403*** | \(-\)0.391*** | \(-\)0.404*** | ||

(0.106) | (0.100) | (0.121) | (0.112) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | 0.487** | 0.418* | 0.457* | 0.469** | ||

(0.222) | (0.240) | (0.233) | (0.218) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.423*** | \(-\)0.426*** | \(-\)0.396** | \(-\)0.449** | ||

(0.136) | (0.133) | (0.157) | (0.171) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | \(-\)0.370** | \(-\)0.358** | \(-\)0.345** | \(-\)0.420*** | ||

(0.136) | (0.138) | (0.139) | (0.111) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.508*** | 0.492*** | 0.508*** | 0.392*** | ||

(0.073) | (0.071) | (0.077) | (0.063) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | 0.079* | 0.073* | 0.069 | 0.070** | ||

(0.043) | (0.040) | (0.045) | (0.032) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | 0.076 | 0.058 | 0.062 | \(-\)0.008 | ||

(0.066) | (0.067) | (0.068) | (0.054) | ||||

\(\ln (\sigma ^{2}_{g,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.144 | \(-\)0.133 | \(-\)0.152 | \(-\)0.138* | ||

(0.085) | (0.089) | (0.097) | (0.078) | ||||

Country fixed effect | No | No | No | No | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 120 | 120 | 120 | 120 | |||

\(R^{2}\) | 0.875 | 0.881 | 0.876 | 0.905 | |||

Specification \(\hbox {tests}^{\textrm{b}}\): | |||||||

Ramsey (1969) Reset | 0.541 | 0.436 | 0.718 | 0.333 | |||

\(\beta _{{\mathcal {E}},-3} =\beta _{{\mathcal {E}},-2} = \beta _{{\mathcal {E}},-1}=0\) | |||||||

\(\beta _{{\mathcal {E}},0} =\beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) |

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(9) | (11) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.711** | \(-\)0.697** | \(-\)0.732** | |||

(0.243) | (0.270) | (0.302) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.710** | \(-\)0.809** | \(-\)0.475 | |||

(0.312) | (0.353) | (0.411) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.574 | \(-\)0.806 | \(-\)0.218 | |||

(0.372) | (0.482) | (0.314) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.722** | \(-\)0.703** | \(-\)0.746* | |||

(0.283) | (0.298) | (0.401) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)1.091*** | \(-\)1.029*** | \(-\)1.070** | |||

(0.310) | (0.336) | (0.392) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.694* | \(-\)0.348 | \(-\)1.387*** | |||

(0.332) | (0.359) | (0.322) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.376 | \(-\)0.422* | \(-\)0.412 | |||

(0.262) | (0.204) | (0.518) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.495*** | \(-\)0.495*** | \(-\)0.504*** | \(-\)0.467*** | ||

(0.066) | (0.065) | (0.067) | (0.070) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.260*** | \(-\)0.261*** | \(-\)0.242*** | \(-\)0.258*** | ||

(0.065) | (0.070) | (0.070) | (0.082) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | \(-\)0.104 | \(-\)0.104 | \(-\)0.109 | \(-\)0.123 | ||

(0.162) | (0.162) | (0.188) | (0.193) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.151 | \(-\)0.148 | \(-\)0.100 | \(-\)0.139 | ||

(0.120) | (0.130) | (0.129) | (0.155) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | 0.011 | 0.008 | 0.015 | 0.021 | ||

(0.087) | (0.098) | (0.093) | (0.108) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.608*** | 0.608*** | 0.630*** | 0.587*** | ||

(0.027) | (0.028) | (0.033) | (0.048) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | \(-\)0.037 | \(-\)0.036 | \(-\)0.024 | \(-\)0.006 | ||

(0.035) | (0.035) | (0.034) | (0.035) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | \(-\)0.001 | \(-\)0.001 | \(-\)0.015 | \(-\)0.001 | ||

(0.045) | (0.047) | (0.046) | (0.042) | ||||

\(\ln (\sigma ^{2}_{g,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.064 | \(-\)0.065 | \(-\)0.057 | \(-\)0.064 | ||

(0.052) | (0.052) | (0.054) | (0.048) | ||||

Country fixed effect | Yes | Yes | yes | Yes | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 200 | 200 | 200 | 200 | |||

\(R^{2}\) | 0.873 | 0.873 | 0.877 | 0.887 | |||

Specification \(\hbox {tests}^{\textrm{b}}\): | |||||||

Ramsey (1969) Reset | 0.388 | 0.387 | 0.432 | 0.845 | |||

\(\beta _{{\mathcal {E}},-3} =\beta _{{\mathcal {E}},-2} = \beta _{{\mathcal {E}},-1}=0\) | 0.915 | 0.905 | |||||

\(\beta _{{\mathcal {E}},0} =\beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) | 0.026 | 0.052 |

Variables | Coefficient | \(\hbox {Estimates}^{\textrm{a}}\) | |||||
---|---|---|---|---|---|---|---|

(12) | (14) | ||||||

All | Core | Periphery | All | Core | Periphery | ||

\({\mathcal {E}}_{i,t}\) | \(\beta _{{\mathcal {E}}}\) | \(-\)0.524*** | \(-\)0.311** | \(-\)0.723*** | |||

(0.169) | (0.141) | (0.201) | |||||

\({\mathcal {E}}_{i,T_{0}}\) | \(\beta _{{\mathcal {E}},0}\) | \(-\)0.531 | \(-\)0.524* | \(-\)0.403 | |||

(0.311) | (0.295) | (0.424) | |||||

\({\mathcal {E}}_{i,T_{0}+1}\) | \(\beta _{{\mathcal {E}},1}\) | \(-\)0.386 | \(-\)0.492 | \(-\)0.212 | |||

(0.283) | (0.299) | (0.366) | |||||

\({\mathcal {E}}_{i,T_{0}+2}\) | \(\beta _{{\mathcal {E}},2}\) | \(-\)0.506** | \(-\)0.303 | \(-\)0.798*** | |||

(0.205) | (0.202) | (0.211) | |||||

\({\mathcal {E}}_{i,T_{0}+3}\) | \(\beta _{{\mathcal {E}},3}\) | \(-\)0.824*** | \(-\)0.543* | \(-\)1.036*** | |||

(0.243) | (0.294) | (0.240) | |||||

\({\mathcal {E}}_{i,T_{0}+4}\) | \(\beta _{{\mathcal {E}},4}\) | \(-\)0.582** | \(-\)0.080 | \(-\)1.637*** | |||

(0.273) | (0.250) | (0.195) | |||||

\({\mathcal {E}}_{i,T_{0}+5}\) | \(\beta _{{\mathcal {E}},5}\) | \(-\)0.255 | \(-\)0.260 | \(-\)0.460 | |||

(0.307) | (0.234) | (0.415) | |||||

\(\ln (\sigma ^{2}_{e,i,t})\) | \(\alpha _{e}\) | \(-\)0.417*** | \(-\)0.437*** | \(-\)0.436*** | \(-\)0.360*** | ||

(0.080) | (0.084) | (0.085) | (0.078) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{g}\) | \(-\)0.430*** | \(-\)0.420*** | \(-\)0.389*** | \(-\)0.441*** | ||

(0.116) | (0.115) | (0.117) | (0.115) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{g,i,t})\) | \(\alpha _{e,g}\) | 0.169 | 0.073 | 0.147 | 0.027 | ||

(0.188) | (0.192) | (0.222) | (0.204) | ||||

\(\ln (\sigma ^{2}_{e,i,t})^{2}\) | \(\alpha _{e,e}\) | \(-\)0.348*** | \(-\)0.306** | \(-\)0.300** | \(-\)0.283** | ||

(0.117) | (0.125) | (0.136) | (0.119) | ||||

\(\ln (\sigma ^{2}_{g,i,t})^{2}\) | \(\alpha _{g,g}\) | \(-\)0.152 | \(-\)0.128 | \(-\)0.124 | \(-\)0.115 | ||

(0.163) | (0.158) | (0.184) | (0.174) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\beta _{2}\) | 0.593*** | 0.587*** | 0.622*** | 0.525*** | ||

(0.067) | (0.069) | (0.078) | (0.069) | ||||

\(\ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})^{2}\) | \(\beta _{2,2}\) | 0.013 | 0.003 | 0.039 | 0.069 | ||

(0.078) | (0.075) | (0.075) | (0.072) | ||||

\(\ln (\sigma ^{2}_{e,i,t}) \times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{e,2}\) | 0.030 | 0.020 | 0.010 | 0.001 | ||

(0.078) | (0.076) | (0.078) | (0.061) | ||||

\(\ln (\sigma ^{2}_{g,i,t})\times \ln (\sigma ^{2}_{\pi ,i,t}/\sigma ^{2}_{x,i,t})\) | \(\gamma _{g,2}\) | \(-\)0.033 | \(-\)0.030 | \(-\)0.004 | \(-\)0.000 | ||

(0.095) | (0.092) | (0.095) | (0.083) | ||||

Country fixed effect | No | No | No | No | |||

Time fixed effect | Yes | Yes | Yes | Yes | |||

N | 20 | 20 | 20 | 20 | |||

Number of observations | 120 | 120 | 120 | 120 | |||

\(R^{2}\) | 0.904 | 0.908 | 0.907 | 0.928 | |||

Specification \(\hbox {tests}^{\textrm{b}}\): | |||||||

Ramsey (1969) Reset | 0.184 | 0.199 | 0.299 | 0.713 | |||

\(\beta _{{\mathcal {E}},-3} = \beta _{{\mathcal {E}},-2}= \beta _{{\mathcal {E}},-1}=0\) | |||||||

\(\beta _{{\mathcal {E}},0} =\beta _{{\mathcal {E}},1}= \dots =\beta _{{\mathcal {E}},5}=0\) |

### 5.2 Using the HP filter

### 5.3 Shock identification with timing restrictions

## 6 Discussion

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