Can the sectoral New Keynesian Phillips curve explain inflation dynamics in the Euro Area?

Abstract

There is no a priori reason to suppose that price-setting behaviour is homogeneous across sectors and countries. Aggregate data are, however, commonly used to estimate the New Keynesian Phillips curve (NKPC), which may very well yield erroneous results if price-setting behaviour is heterogeneous. In this paper, we therefore estimate the hybrid NKPC for the Euro Area using a novel sectoral data set containing quarterly observations from 1999Q1 to 2012Q1. We show that a positive relationship between inflation and real marginal cost cannot be established empirically for a majority of countries and sectors. We also perform a meta-analysis by combining the results of individual significance tests in order to assess the validity of the NKPC in each country across all sectors and in each sector across all countries. We find no empirical evidence for the NKPC in the Euro Area when this meta-analysis is used. Our results therefore raise doubts about the appropriateness of the NKPC for the analysis of inflation dynamics and monetary policy in the Euro Area.

Appendices

Appendix 1

See Tables 8, 9, 10, 11, 12 and 13.

Table 8 Description of sectors used in estimation

Table 9 Descriptive statistics for countries

Table 10 Descriptive statistics for sectors

Table 11 List of variables used to estimate the factors

Table 12 BSQT results for sector-specific inflation and labour shares

Table 13 Correlations between inflation and labour shares

Appendix 2: A wavelet-based procedure for outliers correction

The data are corrected for additive outliers employing a procedure based on wavelet analysis. The principal idea is to decompose the time series into different frequency components, which is in essence a band pass filtering.¹⁶

We transform the data using a maximal overlap discrete wavelet transform (MODWT). The first-level wavelet coefficients correspond to the vector of detail coefficients ${\mathbf {D}}_1 =\left( {d_{1,1}, d_{1,2}, \ldots d_{1,N}} \right)$ and the approximation coefficients ${\mathbf {A}}_1 =\left( {a_{1,1}, a_{1,2}, \ldots , a_{1,N}}\right)$, where $N$ is the number of wavelet coefficients. We use the Haar wavelet filter as there is no need to employ a smoother wavelet filter for outlier detection (Granè and Veiga 2010).

The first-level detail coefficients ${\mathbf {D}}_1$ are very sensitive to any kind of abrupt changes in data, such as presence of outliers. Therefore, it is sufficient to screen only the finest-scale detail coefficients (Bilen and Huzurbazar 2002; Granè and Veiga 2010). Following Bilen and Huzurbazar (2002), the detail coefficients in ${\mathbf {D}}_1$ are compared with a threshold limit given by

$$\begin{aligned} \tau _1 =\hat{\sigma }_1 \sqrt{2\ln \left( N \right) }, \end{aligned}$$

(8)

where $\hat{\sigma }_1$ is the mean of the absolute deviations from the median based on the finest-scale detail coefficients

$$\begin{aligned} \hat{\sigma }_1 =N^{-1}\sum \limits _{n=1}^N \left| {d_{1,n} -M_1} \right| , \end{aligned}$$

(9)

where $M_1$ is the median of ${\mathbf {D}}_1$. Outlier correction is carried out by setting to zero those detail coefficients which exceed the threshold limit $\tau _1$. Formally, a hard-thresholding procedure is performed and the modified finest-scale detail coefficients $\tilde{{\mathbf {D}}}_1 =\left( {\tilde{d}_{1,1},\tilde{d}_{1,2},\ldots \tilde{d}_{1,N}}\right)$ are obtained as $\tilde{d}_{1,n} =0$ if $\left| {d_{1,n}} \right| >\tau _1$ and $\tilde{d}_{1,n} =d_{1,n}$ otherwise for $n=1,\ldots ,N$. Finally, the time series are reconstructed by applying inverse maximal overlap discrete wavelet transform (IMODWT) using the modified detail coefficients $\tilde{{\mathbf {D}}}_1$ and the original approximation coefficients ${\mathbf {A}}_1$.