Has there been any structural convergence in the transmission of European monetary policies?

Abstract

This paper makes three contributions. First we present a technique by which the monetary transmission mechanism of Germany, France, the UK and the Eurozone can be decomposed into its component cycles, compared across economies and across time. As a result, we found that the individual data generating processes have varied over time. Second we show that Germany has now converged on the rest of Europe and not vice versa, although Germany had dominated monetary policy making in Europe for many years. Third, we show that the UK as an outsider has behaved like a peripheral EMU country, even when EMU was not in place. In other words, the transmission mechanisms of Germany and the UK were fundamentally different. Hence, when that German monetary policy dominated Europe in a way that was not in line with the rest of Europe, never mind the UK, it is no surprise that the UK eventually left the ERM (1992). The current financial crisis may enforce the trend of convergence of the transmission mechanism. But there have been signs of a divergence between core and periphery, to some extent involving the UK, so this general convergence, as opposed to tighter convergence in the core, may not last.

Appendices

Appendix 1: Short time fourier transform

Consider a signal s(τ) and a real, even window w(τ), whose Fourier transforms are S(f) and W(f) respectively. To obtain a localised spectrum s(τ) at time τ = t, we multiply the signal by the window w(τ) centred at time τ = t. We obtain

$$ {\text{s}}_w \left( {{\text{t,}}\tau } \right) = {\text{s}}\left( \tau \right)w\left( {\tau - {\text{t}}} \right) $$

(A.1)

We then calculate the Fourier transform w.r.t. τ which yields

$$ {\text{F}}_{s}^{w} \left( {{\text{t}},{\text{f}}} \right) = \mathop {\text{F}}\limits_{{\tau \to {\text{f}}}} \left\{ {{\text{s}}\left( \tau \right)w\left( {\tau - t} \right)} \right\} $$

(A.2)

${\text{F}}_{\text{s}}^w \left( {{\text{t}},{\text{f}}} \right)$ is the STFT. It transforms the signal into the frequency domain across time. It is therefore a function of both. Using a bilinear kernel and a Gabor transform (the time series is stationary, but may contain parameter changes), Boashash and Reilly (1992) show that the STFT can always be expressed as a time-varying discrete fast-Fourier transform calculated for each point in time. That has the convenient property that the “traditional” formulae for the coherence or the gain are still valid, but have to be recalculated at each point in time. The time-varying spectrum of the growth rate series can therefore be calculated as (see also: Lin 1997):

$$ {\text{P}}_{\text{t}} \left( \omega \right) = \frac{{\sigma^2 }}{{\left| {1 + \sum\limits_{{{\text{i}} = 1}}^9 {\alpha_{{{\text{i}},{\text{t}}}} \exp \left( { - {\text{j}}\omega {\text{i}}} \right)} } \right|_t^2 }} $$

(A.3)

where ω is angular frequency and j is a complex number and α are the estimated coefficients. The main advantage of this method is that, at any point in time, a power spectrum can be calculated instantaneously from the updated parameters of the model (see also Lin 1997). Similarly, the power spectrum for any particular time interval can be calculated by averaging the filter parameters over that interval.

Appendix 2: Statistical results

Note: For reasons of space, the results quoted in the tables describe the final regression done and its diagnostic tests. But the figures which follow display the period by period spectral results.

Fig. 1

Gain between Euro interest rates and German GDP

Fig. 2

Gain between Euro interest rates and the French growth rate

Fig. 3

Gain between EMU growth rate and Euro interest rates

Fig. 4

Gain between the UK growth rate and Euro interest rates

Table 1 Regression results: German growth rate and Euro interest rates

VAR/System—Estimation by Kalman Filter
Dependent Variable	DLGERGDP	Quarterly Data From	1977:01 To 2007:02
Usable Observations	122	Std Error of Dependent Variable	7.344034908
R2	0.98837	Standard Error of Estimate	4.953864717
Mean of Dependent Variable	−0.037649496	Sum of Squared Residuals	2871.2707493
Akaike (AIC) Criterion	0.68802	Ljung-Box Test: Q*(21)	33.0404
Variable	Coeff	Std Error	T-Stat
Constant	0.92915083	0.069017425053	13.46255430988
DLGERGDP{1}	−0.83350102	0.862330010393	−0.966568496268
GERINT	−0.51877805	0.180640176422	−2.87188631575
GERINT{1}	0.12575100	0.037446995505	3.358106480903

Table 2 Regression results: the French growth rate and Euro interest rates

VAR/System—Estimation by Kalman Filter
Dependent Variable	DLFRGDP	Quarterly Data From	1972:01 To 2008:01
Usable Observations	144	Std Error of Dependent Variable	1.8633178724
R2	0.99882	Standard Error of Estimate	5.7263454851
Mean of Dependent Variable	0.0083842572	Sum of Squared Residuals	4623.5355987
Akaike (AIC) Criterion	0.70189	Ljung-Box Test: Q*(26)	35.7327
Variable	Coeff	Std Error	T-Stat
Constant	0.14457851	0.030366950564	4.7610481630
DLFRGDP{2}	3.03444661	2.248747036208	1.349394378080
FRINT	0.18960241	0.012935754672	14.65723611884
FRINT{1}	−0.217076786	0.072575370699	−2.99105302958

Table 3 Regression results: the EMU growth rate and Euro interest rates

VAR/System—Estimation by Kalman Filter
Dependent Variable	DLEMUGDP	Quarterly Data From	1970:01 To 2008:01
Usable Observations	145	Std Error of Dependent Variable	1.8916279266
R2	0.40258	Standard Error of Estimate	2.6225880721
Mean of Dependent Variable	0.0023331688	Sum of Squared Residuals	962.91554742
Akaike (AIC) Criterion	0.01512	Ljung-Box Test: Q*(24)	22.6655
Variable	Coeff	Std Error	T-Stat
Constant	−0.09454859	0.038465000620	−2.45804203950
DLEMUGDP{3}	−0.76789776	2.549985465622	−0.301138094484
EMUINT	0.12742306	0.076250929192	1.671101732675
EMUINT{1}	−0.26594720	0.035038487742	−7.59014483447

Table 4 Regression results: the UK growth rate and Euro interest rates

VAR/System — Estimation by Kalman Filter
Dependent Variable	DLUKGDP	Quarterly Data From	1966:01 To 2008:01
Usable Observations	169	Std Error of Dependent Variable	4.3055685240
R2	0.98995	Standard Error of Estimate	4.9772938011
Mean of Dependent Variable	0.0023204919	Sum of Squared Residuals	4038.0729340
Akaike (AIC) Criterion	0.20073	Ljung-Box Test: Q*(26)	20.2142
Variable	Coeff	Std Error	T-Stat
Constant	0.685210687	1.171592652093	0.584854032314
DLUKGDP{2}	0.817373815	2.650584706442	0.308374907941
DLUKGDP{8}	−0.120035372	0.023446142261	−5.11962142703
UKINT{2}	0.163644836	0.033876378444	4.830647294398
UKINT{5}	−0.310839329	0.055562194434	−5.59443938632